分かる (wakaru) v5r,vi. - (1) to understand; to grasp; (2) to know; to realize
This is one of those great words, because it's so easily applicable. "Wakaru?" or "Wakarimasu ka?" (varying the formality level from lower to higher, there), for "Do you understand?" The rejoinder would be "Wakaranai." (often slurred to "Wakannai.") or "Wakarimasen." if you don't understand.