They have very similar meanings, but jump is more of a vertical movement while leap is vertical plus a forward movement. So leap is more often used when describing an energetic movement into something or somewhere while jump has more of a connotation of standing in one place but moving up and down.

From the New Oxford American Dictionary on my Apple computer: leap = jump or spring a long way, to a great height, or with great force: I leaped across the threshold | figurative : Fabia's heart leapt excitedly. move quickly and suddenly: Polly leapt to her feet.

I think "JUMP" is much more commonly used, especially in conversation. "LEAP" is used in literature, and sometimes to refer to longer distances.