The kanji meaning for Kata is made up of three simple characters. The one in the upper left means 'Shape'. The one on the upper right means 'Cut'. The one on the bottom means 'Ground'. So therefore a Kata is a shape that cuts the ground.

The Kata is an artistic presentation in which all movement is defense and counters attack, and put together in a refined manner with no wasted effort. It is a sequence of movements, which are both defensive and attacking, performed as a result of several attacks.

Kata is a term meaning mould, model, style, shape, form, or data-type.
A Karate Kata is a set number of basic techniques arranged in order. Each Kata has its own character. Some Kata have a very heavy, solid, and robust feeling to them. While performing them you can imagine that you are ploughing through the enemy like a bull that cannot be stopped. Other Kata have a quick, light feeling to them and require acrobatics. When performing these Kata you can imagine yourself moving about from enemy to enemy so quickly that you never even get a good look at whom you are fighting. Some are more graceful and flowing in nature, and others are performed very slowly with great muscle tension. Each and every technique is executed as if it were the only technique to be performed and maximised to its fullest. Rather, it is the shape of the techniques, the speed at which they are performed, and the rhythm of the Kata itself that lends it character.

Interpretations of each Kata would reflect on the concepts of the written (kanji) form.
Basically a Kata is a set of prearranged fighting techniques put into a set, pattern or form.

Karate Kata can be split into three schools:

SHURI-TE: Pinan (Heian) Shodan, Pinan (Heian) Nidan, Pinan (Heian) Sandan, Pinan (Heian) Yodan, Pinan (Heian) Godan. Naifanchi. (Tekki) Shodan, (Tekki) Nidan, (Tekki) Sandan. Passai (Bassai) Dai, Sho. Ku-Shanku (Kanku) Dai, Sho, Shiho-ku-shanku. Ji-tte (Jutte). Ji-in. Ji-han (Jion). Gojushi-ho Dai, Sho.

NAHA-TE: Sanchin. Tensho. Gekisai-Dai-ichi, Gekisai-Dai-ni. Saifa (Sai-hawah). Seisan. Seipai. Sanseiru. Shisochin. Kururunfa (Kururun-hawah). Seienchin. Suparinpei.

TOMARI-TE: Chinto (Gankaku). Rohai (Meikyo). Wanshu (Enpi, Empi). Wankan (Matsukaze). Others; Niseishi (Nijushi-ho). Sochin. Ananku. Unsu. Seishan (Hangetsu).
The above-mentioned Kata have some variations. For example, Passai Kata has not only Dai and Sho, but also Matsumura no Passai (Passai of Matsumura), Tomari no Passai and Ishimine no Passai. In Uechiryu, although a Naha-te style, they developed a different series of Kata. These include Sanchin, Kanshiwa, Seishan, Seirui, and Konchin.

Karate Kata which possess numbers as names are considered originally of Chinese and/or Buddhist origin, and passed into the Okinawan-te systems during the 1800's. The numbers have been referred to as many interpretations and factors in modern Martial Arts, either as the amount of steps or techniques etc.

However, it has been said that that they have their history within the original teachings of acupoint striking within the Kata. For example, there are considered 36 'killing' points on the human body (Sanseiru). Many of the 'numeric' Kata have their foundations within the original Chinese acupoint striking system practised in the mid 1500's. It was considered the original method of 'numeric strike-point' combat was created by the Chinese Shaolin Martial Artist Feng-Yiquan at that time. Other Chinese Martial Artists who studied this form of combat included the famous Xie-Zhongxiang.
These 'numeric' Kata also include; Suparimpei (108), Gojushi-ho (54), Sanshiru (36), Nipaipo (28), Niseishi/Nijushi-ho (24), Seipai (18), Seishan/Seisan (13), etc., and are all believed to be linked to the acupoint science.
In Buddhism, however, numbers hold great symbolic importance, specifically referring to the108 desires of man. This is very interesting as many of the Kata hold factors of 108, as: Suparimpei (108), Gojushi-ho (54), Sanseiru (36), Seipai (18), etc.
Karate Kata lineage can be based on the following:
Aragaki - Ni-sei-shi, Sochin, Unsu.
Chatanyara - Ku-Shanku.
Gokenki - Hakucho, Nipaipo, Papuren.
Higaonna - Kururunfa, Saifa, Sanchin, Sanseru, Seienchin, Seipai, Seishan, Shisochin, Suparinpei.
Ishimine - Bassai.
Itosu - Pinan Shodan, Pinan Nidan, Pinan Sandan, Pinan Yodan, Pinan Godan, Bassai-dai, Bassai-sho, Chintei, Chinto, Gojushi-ho, Ji-tte, Ji-han, Ji-in, Kosokun-dai, Kosokun-sho, Naifuanchin Shodan, Naifuanchin Nidan, Naifuanchin Sandan, Rohai Shodan, Rohai Nidan, Rohai Sandan, Shiho-kosokun.
Mabuni Kenwa - Aoyagi, Juroku, Miyojo.
Matsubayashi - Annanko.
Matsumura - Bassai, Seishan, Rohai.
Matsumora - Rohai, Wankan (Matsukaze), Wanshu.
Miyagi - Gekisai-ichi, Gekisai-ni, Tensho.
Mabuni/Ueichi - Shinpa.
A further note regarding 'numeric' Kata. All of the Kata that are named with numbers, for example; Niseishi (24), Seis(h)an (13), Sanshiru (36), Suparimpei (108), Nipaipo (28), Seipai (18), Gojushiho (54) etc., were practiced in China and passed to Okinawa in the 19th century and earlier.
However, historians debate the significance of numbers as Kata names. There are several theories, the simplest being that the number was the number of movements in the Kata when it was created.
However, in ancient China, a charting system was created numbering the vital points on the human body and sets of movements were created to attack these points. As with most cultural phenomenon in China, there is a definite Buddhist influence on some Kata names.
Please remember that in many cases, kanji representations of Kata names are often very recent. Many Kata names were unwritten until late in the last century. Prior to this, Kata names were often passed through oral tradition alone. When Karate-ka wanted to write the kanji down, it may have been the case that the writer didn't know the meaning, and used kanji that he thought represented the Kata in some sensible way (phonetic sound of the Kata name is an obvious possibility), it may not be the original name at all. Because of this, there can sometimes be different kanji for the same Kata, or incorrect kanji altogether.

To develop overall speed, there are several sequential steps in training:

Conditioning
Power development
Skill improvement
Chambering
Speed training

Condition, including flexibility, strength and agility training, is a prerequisite for speed training. The completion of basic conditioning is signaled by a level of fitness that allows the athlete to begin the more intensive exercises that develop explosive power. Exercises for developing explosive power. Once the target muscles start to develop, begin working on skill refinement. Each skill should be examined to eliminate unnecessary movements and increase bio mechanical efficiency.

With highly refined movements and strong muscles, you can begin adding speed to each movement. Start skill loading gradually and observe your body's reaction. If you can add speed and still maintain semi-refined movements, continue to increase your intensity. Eventually you will reach the final stage of speed training in which you can execute skillful movements at high speed.

Now let's examine the four types of speed individually.

Perception speed can be increased by repeatedly exposing yourself to situations that require instant analysis. Law enforcement officers do this by participating in mock confrontations that require them to quickly analyze who demands to be responded to and how. The best drill for developing perception speed in martial artists is sparring.

Sparring teaches you what an attack looks like before it happens. Sparring also teaches you to be alert at all times by placing you in imminent physical danger. Alertness is one of the keys to perception speed. You cannot analyze the situation if you do not realize it exists.

Reaction speed is improved by a two pronged approach. First, you have to be aware of what types of situations may arise in any given environment. In sparring, your opponent does one of several things which are predetermined by the rules of the sparring match. You know in advance what is allowed and what is not.

In a self-defense situation, you also have some idea what to expect. You can reasonably expect your assailant to try to harm you in some way. You do not expect him to start singing songs or reciting poetry. By estimating what to expect from the given environment, you narrow down your choice of possible responses.

Second, you have to have experienced an identical or similar situation before. If you have been attacked hundreds of times by a front kick in sparring, your reaction becomes almost reflexive. If you are sparring for the first time, your reaction time is longer because you must formulate a response without a basis for comparison. If you have practiced self-defense techniques in a realistic way hundreds of times, you are much better prepared than if you spend all of your time beating up a stationary heavy bag.

Execution speed is the type of speed that most Karate practitioners training focus on. Executing techniques like kicks and punches with speed takes up a large part of the intermediate and advanced stages of training. Execution speed can best be improved through attention to detail. Shifting into a ready posture at the last minute wastes time. Begin each movement with a ready and relaxed posture. If you are going to punch, have your hands up and ready. If you are going to kick, shift your weight to supporting leg and relax your kicking leg. Shifting your weight and positioning your hands can take more time than the actual striking or kicking. Anticipate what is necessary and be prepared.

When you learn a new skill, practice it slowly at first, to train your muscles in the correct execution of each movement. When you can execute with little thought about the segments of the movement, speed up gradually. In speeding up the movement, take care not to loose the precision you learned in the beginner stage. Strong basics are essential for speed training.
Observing the laws of motion is also important to execution speed. If you flail your arms and head wildly about when kicking, your kick will be slow. If you stabilize your posture, your kicking speed will increase. If you punch with your arm, your punching will be slow. If you punch from your hips, you’re punching speed and power will increase. If you spin with your upper body tilted to one side, you will lose kick, however, creates a continuous circle of whirling force, increasing the speed of the second kick.

Finally, relax to create speed. Tense muscles have more difficulty responding to your intense demands than relaxed muscles. Relax just prior to the movement and maintain a minimum amount of tension during the movement. Relaxation conserves energy and lessens the amount of force necessary to move your body quickly.

Recovery speed is the result of execution speed. The old adage "what goes up must come down" applies in other directions as well. If your fist shoots out in a punching motion, it must return along the same path to be efficient and effective. If you execute a side kick and drop your leg to the ground immediately following impact, you will be off balance and in danger. You must
Re-chamber the leg and then return to a natural stance.

If you do not execute the recovery portion of the technique, the action becomes "dead." It does not have the dynamic quality associated with speedy movement. It also increases the risk of joint injury tremendously. A fast strike or kick that ends in a locked out position is a common case of knee and elbow injuries.

A complete technique has an initiation, execution, impact and recovery. Each phase must be executed correctly to create dynamic speed.

CAUTIONS
Never use complex skills for speed training.
Always master the basics before moving to speed training.
Never tense your muscles before executing a speed skill.
Muscles must be well trained before engaging in speed training. Weak muscles that cannot bear the intense requirements of speed training are easily injured.