Real meaning of "beg the question"

Normally, when people say the phrase "beg the question," they mean that the issue they're talking about raises an interesting question. So one might say this: "The fact that Brett Favre is still playing begs the question: When the hell will he retire?"

But this is not technically how to use the phrase, although most linguistic purists have all but given up trying to pound it into the heads of the great unwashed (because there are too many of them). To beg the question is actually to "assume the truth that one is attempting to prove." This is quite common in circular reasoning. So a correct example of begging the question might be:

Bill: "God must exist."
Jill: "How do you know?"
Bill: "Because the Bible says so."
Jill: "Why should I believe the Bible?"
Bill: "Because the Bible was written by God."