떨어지다 means falling from a place higher than the ground, like a chair, desk, and so on. 넘어지다 means falling down on the ground while walking or running, tripping over something, etc. 떨어지다 has other related meanings, like 주가가 떨어지다(stock prices fall), 성적이 떨어지다 (school marks fall), 시험에 떨어지다 (fail a test), etc.