The word 'Bunkai' (分解) refers to taking something apart, or analysing something. In the case of Karate, 'bunkai' refers to the application of the movements of the Kata against an opponent, these applications are created by taking apart and analysing the kata.
The Kata do not exist just as a form of exercise for demonstration purposes. They embody a large number of self-defence applications. Without understanding how the self-defence applications are developed from the Kata, the Kata is just a form of dance. Students are taught basic bunkai but many variations exist, and students can even develop their own once they have acquired an understanding of the movements of the kata.
Kata Bunkai
Omote and Ura
The terms "Omote Bunkai" and "Ura Bunkai" refer to "Surface Bunkai" and "Hidden Bunkai" or, basic/simple Bunkai you can come up with as a direct/basic/obvious application of a technique or set of, and Bunkai which are generally more advanced and may be 'buried' in a kata, utilizing "hidden techniques".
Examples
(coming eventually)