It is difficult to give a clear and exacting statement on what is bonsai. I always have this predicament when confronted by this very question.
The uncertainty is compounded by the self-recognition that even after several years of actual practice, I myself am still a beginner who spends so much time analyzing, designing, and redesigning a potential tree that comes my way.
Nevertheless, I always do the explaining, retrieving my store of memory on the subject which has accumulated with time from various readings, conversations, seminars, exhibits, and hands-on experience.
The word bonsai comes from bon, meaning tray or pot, and sai, meaning tree. Literally, therefore, the word should mean potted tree.
However, there are more to it.