Jiu Jitsu is a gentle science and art of grappling and subduing your opponent via a dominant position, joint lock or a strangle. It is gentle, because functional Jiu Jitsu needs to be based on technique, positioning, leverage and timing in order to prevail against physically larger opponents.
It is a science, because the while of body is extensive and the amount of positions, transitions, reversals, submissions and escapes might seem endless, but it is all based on timeless principals that transcend positions and submissions and apply across the board.
It is an art, because the practitioner learns to apply his own individual sense and experience, learning to feel the energy and movement of an opponent and to react with your individual arsenal of clinches, takedowns, positions, strangles and joint locks.
At higher level Jiu Jitsu is like a human chess game, with multilevel attack and counter game. You learn you use your entire body as a means to control your opponent and move them around, while your brain will be solving real time combat puzzles.