Kata

Taikyoku "First Cause"

Five Forms: Shodan, Nidan, Sandan, Yodan, Godan

Translated in the Karate-Do Kyohan as "a philosophical term denoting the macrocosm before its differentiation into heaven and earth: hence, chaos or the void". 

A set of kata developed by Gichin Funakoshi that would enable beginners to learn Basics.

Heian "Peaceful mind"

Five Forms: Shodan, Nidan, Sandan, Yodan, Godan

Known originally by the Okinawan name Pinan, Funakoshi is credited by many with being the first to refer to this kata series by the Japanese word Heian, meaning "Peaceful mind" or "peace and tranquillity." The name change was likely due to the growing national spirit in Japan at that time, causing Funakoshi and others to change Pinan to a Japanese word.

The word Heian was chosen by Funakoshi to demonstrate a philosophy of being confident in one's karate abilities. The thought was that, if you mastered each of the five kata in the series, you could enjoy the peace of mind the kata afforded.

Funakoshi also reversed the order of the first two kata in the original series to reflect the difficulty of the kata.  Hence Heian Shodan is equivalent to Pinan Nidan and Heian Nidan to Pinan Shodan.

Bassai-Dai "To penetrate a fortress"

Two Forms: Bassai-dai (major) and bassai-sho (minor)

Bassai-dai was originally known as passai-dai, but was more commonly referred to as Matsumura-no-passai. The original passai form was developed by Bushi Matsumura, and was one of the first kata taught to Anko Itosu. After years of practicing the kata, Itosu developed the passai-sho form.

Even though the most common interpretation of bassai is "to penetrate a fortress," another translation gives a more descriptive definition of the intention of the kata. Because of the variety of techniques in the kata, one of the best interpretations of bassai is "to break through the enemy's defences by shifting and finding the weak points." Although this is not a literal translation, it is ultimately the true meaning of the kata.

Kwanku To view the heavens"

Two Forms: Kwanku-dai (major) and Kwanku-sho (minor)

The name describes the opening move in the kata whereby the practitioner literally views the sky through their hands.

Kwanku is one of the oldest forms practiced today. The original name for this kata was Ku Shanku.  Ku Shanku was a Chinese official and martial artist stationed in Okinawa. It is not known if he was sent to Okinawa by his government to spread martial arts, or was simply on a diplomatic assignment.  He eventually stayed in Okinawa for at least five years and taught karate to many individuals, the greatest of whom may have been Tode Sakugawa.

When Ku Shanku was transferred back to China, he left behind many students but only one official kata, which eventually was named after him. From this form, Sakugawa developed many others as he disseminated this early style of karate.

It was, however, Anko Itosu, and not Sakugawa, who probably discovered the most from his practice of Ku Shanku. Around 1900, Itosu was asked to teach karate in the Okinawan school system. Because he thought the Ku Shanku kata was too difficult for elementary school children, he developed the pinan kata series from Ku Shanku over a five year span.

Funakoshi introduced it to his Japanese students and changed it's name to Kwanku.  

Hangetsu  "Half Moon"

Originally known as Sesan, has many crescent-shaped techniques, stances and stepping routines, which is why it was later named "half moon".

Jion

Jion is the name of both a Buddhist temple and a patron saint of Buddhism and is thought to have been developed by a Chinese monk who learned his art in the Jion temple.

Ji'in "Temple Grounds"

Ji'in, along with Jutte and Jion are from the Shurei school although historically they may have originated with the Tomari-Te system and Matsumura.

Jutte "Ten Hands"

The name implies that one who has mastered this kata is as effective as ten men.

Tekki  "Iron horse" or "Horse riding"

Three Forms: Shodan, Nidan, Sandan

Was originally referred to as Naifanchi meaning "fighting, holding your ground". As the new name implies, this series of kata is performed exclusively out of a straddle or horse-riding stance (kiba-dachi).

The originator of the first tekki kata is unknown, but it is believed that Anko Itosu developed the second and third forms. It was because of the perceived difficulty of  the tekki kata that Itosu decided to develop the Pinan series as the initial forms taught to Okinawan public school students

Meikyo  "Mirror of the soul"

Also known as Rohai which translates to "white heron" or "vision of a crane". This kata is also from Tomari-Te.

Nijushiho  "Twenty Four Steps"

Originally known as "Neseishi", this kata was derived from "Kaisan".

Sochin "To keep the peace"

Origininating from China, it evolved from Naha-te. Naha-te master Ankichi Aragaki left Naha to introduce his style to martial artists in the capital city of Shuri.  By the time he returned, Goju-ryu karate had become the most popular style in Naha. This is a reason that Sochin was more popular in Shuri than it was in Naha.  The version of Sochin that was later introduced to Japan was developed by Funakoshi and his son.

Empi "Flying swallow"

Originally named Wansu, it is one of the only forms left from Okinawan Tomari-te. Tomari-te, and most of its kata and techniques were lost to history due to the secrecy of its practitioners.

Wansu was a Chinese official who arrived in Tomari around 1683 during the reign of King Sho Tei. Wansu was highly adept at martial arts, and this knowledge soon became known to the local population. Little is known about Wansu, however, other than the fact he only taught a few students at a time. After only a few years in Okinawa, Wansu returned to China, leaving his students to fend for themselves. He did, however, leave behind a kata that eventually became known as Wansu (and later Empi).

Wansu was therefore practiced exclusively in Tomari until after 1865, when it spread to both Shuri and Naha. Funakoshi altered the original name to the Japanese word "Empi" in order to describe the upward and downward movements of the kata. These movements, along with the quick shifting of stances, are similar to the movement of a flying swallow, thus its namesake.

Gankaku "Crane on a rock"

Originally known as Chinto, this kata was eventually called Gankaku because of the one-legged stance which is predominant throughout the form.  Gankaku was developed by Anko Itosu.

Gojushiho "54 steps"

Two Forms: Gojushiho-dai (major) and Gojushiho-sho (minor)

Originally known as Useshi, the kata originates from China, but was developed fully by Bushi Matsumura.

The second version; Gojushiho-sho was introduced by Itosu.

Wankan "Crown of a King"

This kata is from Tomari-Te.

Unsu "Hands in the Cloud" or "Cloud defence"

Even if your enemies surround you like a cloud, you will defeat them if you have mastered Unsu.