The medical term for it is 'sleep myoclonus'. It refers to the contraction of muscles that makes you 'jump' rather than any 'feeling' that you get. I'm not sure if you are looking for a less medical word, but that's all I know.
Outside of a disease/condition, it usually occurs as a reaction to some stimulus. Watching a horror film and jumping at a scary part, for example. In the case of sleep, it happens in the early stages of the sleep cycle, normally just before you actually fall asleep and it is also a reaction to a stimulus. The stimulus could be external - something happening in the room as you are falling asleep, or it could be internal - something happening in your dream.