To say that something "begs the question" mean that it assumes its own premise without proof. The alt.usage.english FAQ suggests "Telepathy cannot exist because direct transfer of thought between individuals is impossible" as an example; the late Bill "Whoppers Junior" Safire suggested in 1998 "Lying is wrong because you shouldn't say things that aren't true." as well.
It does not mean "to raise the question." That's something else. More Safire:
Let's say you argue: “Common usage makes it correct because that's the way most people talk.” I say that begs the question because “the way most people talk” is the definition of “common usage.” You could logically argue that “common usage makes it correct because language is changing constantly” or that “common usage makes it correct because rigid prescriptivists have been shown to be the laughingstocks of linguistics,” but you cannot argue in a straight line that “common usage is correct because it's common usage.”Got it? Good. Because we have screwed this up many times.
Dictionaries have long reported that to beg no longer means only “to ask for a handout” or “to entreat humbly,” as in “I beg to differ.” It also means -- especially in the phrases to beg the question or to beg the point -- “to take for granted, to assume without logical proof.” And beyond that, “to avoid the issue; to sidestep the argument.” (Sentence fragments are O.K. when used for stylistic emphasis.)
“I wonder,” wonders Ms Meyers, not begging but asking, “has such frequent misuse of the technical term to beg the question made it somehow a proper use of the phrase? Or does such usage remain mistaken?”
Stay on those ramparts, logical thinkers -- hold the fort for Aristotle, the English language and St. George! To use to beg the question as a synonym for “to call for the question” is a mistake. Why? It's a mistake because it is in error. (That's begging the question.)
poll results, 2/11: I knew what it meant: 46 (58%); I'm ashamed I was so wrong: 15 (19%); and Means the same as "raises the question": 17 (21%).