Kihon (基本, きほん) is a word (Japanese) that means "basics" or "fundamentals" and is used to refer to the basic techniques that are taught and practised as the foundation of most Japanese martial arts.
Kihon kata is prearranged partner drills. Here, two students face either other and alternate execution of a technique. This approach combines repetition with training in distancing. Targets for punching and kicking, such as bags, shields, or dummies, are also commonly used in kihon training to strengthen muscles, bones, and even skin.
Kumite (組手) is a word that  basically means sparring. It is one of the three primary sections of karate training, along with kata and kihon.  Kumite can be used to develop a particular technique or a skill or even used within a competition.
Kata is a word which is a way of describing detailed choreographed patterns of movements. There have been conflicting stories on why this has been created but the most commonly accepted explanatino is that it acts as a reference guide for a set of moves which can then be used in a sparring scenario. The main objective here is to try out different combinations of techniques in a safe manner.