"Faith" is an oft-cited word, particularly against atheist demands for proof of religious claims. But what does it mean?
It clearly can't just mean "this is unprovable", as what is unprovable is, to that extent, unbelievable. I can't prove, one way or the other, that there is a mind-independent reality. So, to the extent that I have no proof, I thus have no belief.
For example, I cannot prove, one way or the other, that tomorrow is going to happen. It might not -- the world might come to an end tonight, for example. And it might well -- after all, in the past, whenver I've wondered about tomorrow, it's gone ahead and happened. Can I really believe that tomorrow is going to happen? Not really; there's no particular content to that belief that I could commit myself to. If I purport to believe that tomorrow will happen, I'm playing a sort of game with myself, deceiving myself. The best I could do is believe that there is a good probability that tomorrow will happen, based on past experience.
(I should probably defend that idea at length; as it would be lengthy, take it as given for this post.)
The most defensible idea of faith I know comes from Kant. Kant argues for a notion of "rational faith", where faith picks up where reason gives out.
For Kant, reason can tell us only about things as they are experienced. This amounts to two slightly different claims. First, reason takes in information about the world through experience, principally sensory experience. Second, reason structures that information, providing a framework -- including such foundational assumptions as space and time -- within which the data of sensory experience can make sense. Together, these functions of reason generate knowledge.
Faith comes into play, in this framework, when the mind tries to go beyond reason, to reach to the limits of what can be thought.
One idea that one must have faith in is the existence of an external, mind-independent world. It's suggested by the fact that we have experiences apparently imposed upon us by something external to the mind. However, we can't know that it's there, in Kant's view, because that would require knowing something apart from the structuring function of reason, which is impossible. However, we can have faith in it, in that we can't help but think of it, and we don't know anything that contradicts it. (Simplifying a lot here, obviously.)
Freedom, in the sense of free will, is a similar idea that we must have faith in. We can't know that we are free -- it's not provable, it's not taught by experience. However, it's a background assumption we all come with which makes action possible at all. If we aren't free, then there's no such thing as real action, only caused bodily movements. So, faith is the available option.
God is a similar idea. God is suggested, not knowable, and thus is something we can have faith in.
I think this idea of faith is defensible. However, it's important to see how weak it is. It puts God outside the realm of what can be known -- permanently. It also makes belief in God optional. Faith is a choice, something that one must will oneself to do, and thus something that one can, rationally, refuse to do.
So, if this is the notion of faith that a theist wants to rely on, then the theist has to concede that atheism is just as sensible a view.