"Begs the question" doesn't mean "begs to ask the question," it's a type of circular argument where a questionable conclusion is already built into the premise.
The most famous example is probably "When did you stop beating your wife?" but it's one of the sneakier common tricks lawyers, cops and evangelicals use on their victims, as well as a staple of science fiction's battles of logic between humans and robots/computers -- typically as the coup de grâce before the machine loops into self-destruction. I can also think of at least two Rush songs that beg the question -- no surprise when a libertarian/drummer is allowed to write lyrics -- but this post is already nerdy enough.
Unless you're writing about any of the above areas, you really shouldn't use the phrase at all; people don't need to know that you're not smart enough to use it correctly.
[You saw what I did there, right?]