Believe it or not, there is no consensus among philosophers about what it means to beg the question. Let me throw in my 25 cents' worth. To beg the question is to use a premise that your interlocutor (the person you're trying to persuade) doesn't accept. Begging the question is an informal fallacy, not a formal fallacy. This means that it (the fallacy) cannot be detected merely through an examination of the form of the argument. It is detectable only through an examination of the content or context of the argument. People beg questions; arguments do not (in themselves) beg questions. Perhaps we should say that people, while arguing, beg questions.
The term "begging the question" (Latin: petitio principii, petitioning for the principle), means asking, or begging, for the proposition that is at issue in the discussion or debate. The idea is that conclusions must be won honestly, through hard work, and not by trickery or subterfuge. If you're trying to persuade me to accept a certain proposition, you must show me that propositions I already accept commit me, logically, to accepting it. Arguing is coercive. It says "Accept this proposition, or else," where the "or else" means "or else you are irrational for believing contradictory propositions." The only leverage an arguer has is the law of noncontradiction. The arguer's aim is to show the interlocutor that there is a logical price to be paid for believing or disbelieving a certain proposition. (Arguing has no effect on people who don't care about irrationality.)
If you use even one premise that I don't accept, then you have given me no reason to accept your conclusion. This means that you have wasted your precious time (and mine).
Example: Suppose, as is in fact the case, that I am not a utilitarian, but that you try to persuade me that act x is right by showing me that the rightness of x follows logically from utilitarianism and certain other premises. What reason have I to accept your conclusion? I will simply point out that I am not a utilitarian. You are asking me to concede something (utilitarianism) that I am unwilling or unprepared to concede. You may well be able to persuade me that x is right, but it will have to be with a different argument, one whose premises I do accept. You will need to find out what my normative ethical theory is and use it as a premise. This doesn't mean that you will succeed; it means that this is the only argument that has a chance of succeeding (with me).
One nice feature of this analysis of begging the question is that it explains how someone can argue from premises that he or she doesn't accept. Suppose that I am a Kantian in ethics and that you know this. Even if you are not a Kantian (you may be a utilitarian), you may use a Kantian premise to persuade me to accept the conclusion that x is right. There is nothing disreputable about this argumentative technique (though I have heard people suggest as much). It is used by philosophers every day. It's called "playing devil's advocate," or "assuming something for the sake of argument."
Philosophers, as such, are interested in logical relations between propositions, not in the truth of propositions, or rather, not in the truth of contingent propositions. Philosophers are perfectly qualified, by their training, to tell someone which propositions are necessarily true and necessarily false. Contingent propositions are those that are neither necessarily true nor necessarily false. The proposition that the Texas Rangers won the 2017 World Series is a contingent proposition. It happens to be false, but my philosophical training has nothing to do with my knowing that. The proposition that all bachelors are eligible to be married, on the other hand, is a necessarily true proposition; my philosophical training has everything to do with my knowing that.
If what I am saying about begging the question is correct, then it's in every prospective arguer's interest (which means every person's interest) to understand as many normative ethical theories or doctrines as he or she can. If I am well-versed in, say, 12 normative ethical theories (as indeed I am), then I am in a position to persuade adherents of any of the 12 theories of some normative proposition, such as that it is wrong to eat meat. The more theories or doctrines one understands, the more effective an arguer one is (or can be).
I mentioned earlier that people, and not arguments, beg questions. This means that, with the same argument (understood as a structured set of propositions), I may beg the question against interlocutor A but not against interlocutor B. Suppose I argue that the wrongness of eating meat is entailed by utilitarianism plus certain factual premises. If A is a utilitarian and B a Kantian, then I beg the question against B but not against A. I have used a premise that B does not accept, indeed, cannot accept, given the contrariety of the theories. (Two propositions or theories are contraries when they cannot both be true but may both be false.)
Whether one begs the question is context-dependent, with the main contextual element being the beliefs of one's interlocutor.
