A jump cut is an editing transition which cuts between different moments in the same scene, missing out some bits of the action and thereby creating discontinuity. For example, have a look at these jump cuts in a scene from 'Erin Brockovich':
The effect of this is to create a sense of the character's emotional turmoil and choatic state of mind. The editing reflects what is happening to the character psychologically.
The following two clips are from a documentary about film editors - they contain a wealth of information about the hitsory, techniques and effects of editing, and you should definitely watch them.