In its original and proper meaning, this phase refers to the act of assuming the truth of what you're trying to prove. It's a logical fallacy. (When I tried to put it in the original Latin, my spell-check refused my attempt. So I'll just spell it out: p-e-t-i-t-i-o p-r-i-n-c-i-p-i-i.)
But in recent times the phrase has come to be used in a quite different way. For example, "That begs the question, should Trump be impeached?" (For what it's worth, the correct answer is probably "Maybe, but not in the way some in the House are going about it." But that is by the bye.)
Using the phrase in this second way is a crime against logic. What the speaker or writer is trying to say is, "That raises the question, should Trump," etc. The crime is that in using the phrase, one is keeping oneself from ever using the phrase in its right way.
For more on this issue, a trip to Google shows that "begging the question" calls up a long panoply of sites. For example, try begthequestion.info for a clever treatment of this common mistake.
Show off your vocabulary skills! Don't appear to be a dolt! Show off your logic chops!