The language of karate is Japanese just as the language of music is Italian. Italian words such as andante and allegro are understood by musicians all over the world, so words such as gyakuzuki and maegeri transliterated from Japanese, are understood by students of karate everywhere. The three Ks of karate are Kata, Kihon, and Kumite.
Originally, in Okinawa, where the art was first developed, karate was taught in secret to small numbers of students, and nothing was written down. The student practised techniques of attack and defence in formal sequences, performed solo, towards imaginary assailants attacking from all directions. The attacking techniques include punches and many other blows with the hands and fingers as well as several different kinds of kick. The defences include blocking and deflecting blows, and body-shifting to avoid blows and kicks.
The whole body is trained to move quickly, to turn, to jump, to strike and to kick. These formal exercises are kata. A style of karate may use one or a few kata, and some styles have many kata each of which emphasises a style of fighting, or the use of a particular repertoire of techniques. Originally, the movements of a single sequence, a single kata, were repeated and repeated, perhaps for a year or more until the sequence could be performed perfectly. When one kata was perfected the student moved on to another. The whole of karate was kata, and the only application of karate was in lethal fighting.
Gichin Funakoshi was a native of Okinawa and studied karate when it was still secret. Convinced of its effectiveness he went to mainland Japan to demonstrate his art. On the mainland there were many schools of empty hand fighting, ju-jutsu, with long lineages. The art and sport of Judo (ju-jutsu purged of the lethal elements) was already established, and an example of how an ancient art could be tamed and made available to the wider Japanese public as a sport.
Funakoshi's karate was astoundingly effective and caused a sensation: it was as if a traditional fiddler from Orkney turned up able to out-play the violinists of the Berlin Philharmonic Orchestra. Many more people wanted to be taught by him than he could teach using the traditional method of practising kata in small groups, so following on from the methods developed in judo he broke the techniques of kata into the basic units of punches, blocks, and kicks, and began teaching these to beginners. The Japanese word for basic is kihon; and kihon is what you study first when you begin karate.
The third K of karate is sparring, kumite. Two or more people exchange attacks and defences. Funakoshi's tradition ignored this form of training though other schools of Okinawan karate, such as Motobu kenpo, practised kumite as well as kata. Kumite was eventually introduced into the Shotokan style.
When kumite is taught to beginners it is pre-arranged. A specific attack is announced and the defender responds with a specific defence. This teaches the student to choose the correct distance and the timing of attacks and defence, and is the fore-runner of free sparring in which two people exchange attacks and defences as though in a fight, though the attacks are controlled to minimise injury if the defences fail.