The article on question-begging in Wikipedia is not particularly good as it currently stands. In fact the first paragraph contradicts itself. The lede for the article on circular reasoning is better.
Originally, what is translated into English as begging the question, refers to a fault in a dialectical argument in which the speaker assumes some premise that has not already been demonstrated to be true, or is not accepted as true by the other party. One form of question-begging involves using a premise that is so similar to the conclusion that in effect it assumes the conclusion itself. It is therefore closely related to circular reasoning.
A common definition is that a question-begging argument is one in which an argument's premises assume the truth of the conclusion. This is problematic because in any deductively valid argument, one might say that the premises always include the conclusion, albeit maybe indirectly. But we would not want to say that all valid arguments beg the question.
A better account would be to say that in a persuasive argument, one has better reasons or grounds to accept the premises than one has for accepting the conclusion. Therefore there is a flow of justification from the premises towards the conclusion. The premises support the conclusion. In a question-begging argument there is no such flow: there is no better reason to accept the premises than one already has to accept the conclusion.
Question-begging is not a formal fallacy, but an epistemic failing. In fact, question-begging or circular arguments are valid, since if the premises hold, the conclusion follows by necessity.
