What are the beejebers?

Answer 1

There isn't really anything called a bejeeber. It is just a saying... "you scared the bejeebers out of me." It means that they were very surprised and scared for a short period of time, because they weren't expecting you, or didn't see you, or something. The dictionary lists it, but under an archaic spelling/pronunciation: http://dictionary.reference.com/search?r=2&q=bejabers

Answer 2

The word bejebers is believed to be a mutation of the Irish word bejabers. It is used as a mild expletive, variously meaning the devil, poop, or fear. In former times, it was an acceptable word to use in place of coarse vulgarities.