Firstly it probably helps to distinguish what philosophers mean by this slightly strange phrase when compared to something people say quite frequently that sounds very similar.

When someone says “that begs the question…” it usually means something like “well that makes me wonder about…”. For example:

Andy Murray only looks good on grass, which begs the question whether he can ever be ranked much higher than number 4 in the world…

Unfortunately for us, this doesn’t really have anything to do with what philosophers mean when they use these words together. When a philosopher suggests that a given argument is ‘begging the question’, they are claiming that it contains an assumption (probably implicit or hidden) in the premises that is necessary in arriving at the argument’s conclusion.

The Pan Dictionary of Philosophy defines ‘begging the question’ as

The procedure of taking for granted, in a statement or argument, precisely what is in dispute.

So an example might run something like this:

I know I am free. Whenever I have a tough decision to make I sit down, think about my options and opt for one on the courses of action.

This might not be the best example, but if we sort it all out it begins to look like this:

1. I make reasoned decisions.

C: These decisions are free.

But really what is happening here, is a bit more like this:

1. I make reasoned decisions.

2(implied). The fact I have this experience of weighing up options mean my decisions are free.

C: These decisions are free.

Now of course, 2 is exactly what philosophers would be looking to challenge if they were disputing that our writer has free will so, this is begging the question.