The problem with reading much of these older texts, be they Greek or Buddhist, is that I'm reading English translations. While English is a very diverse language there are several concepts that it often fails to accurately capture or convey. At other times, many of our words carry a certain amount of historical or social baggage that distorts the actual connotation in which the original author was conveying the concept being discussed. This is, in my opinion, what seems to be the case with Buddhist faith. Because really faith isn't the right word, and this slowly became apparent as I read more into the sutras. A much better translation would be trust, not unfounded blind faith, but a trust that is gained through reason and deduction, observation and analysis.
This concept in Buddhism is most often brought up in relation to the Dhamma, the Buddhas teaching, and the trust that is placed in a teacher. It is the same kind of trust one puts in a map or guide if you were trying to reach a difficult geographic location. You haven't been to where you're going, you don't know the way, you don't know how to prepare or what to expect. You choose a map based on it's accuracy, on suggestions from other travelers, on its detail and its relevance to where you are trying to get to. While looking at it in a store it may give you an idea of where you are going, it becomes invaluable on the actual trail when faced with questions as to which trail to take, where to stop for the night or how much longer a steep climb may last. In the same way the Buddha asks that if it seems legit we should trust that the Dhamma can act as a map in our life. He advises that we use it, see that it works, and if we reach a point where our path isn't clear choose to follow the Dhamma, use it as a map to get to where you want to go.
In the same way the virtue of faith is often applied to ones teacher. This trust is gained by questioning him, observing him, and an ongoing amount of healthy skepticism. The faith or trust in ones teacher though comes when, like a guide in the wilderness, you have to take his word that he knows where he is going. That the training he is recommending, while the initial benefits or the eventual goal may not be initially clear you need to have a certain amount of trust that it will at some point make sense, that although the route taken does not seem at first to make sense, that once the peak is gained the route below will be clear, and you can see that the approach was in fact the most sensible.
When discussing the tests of student should put his teacher through to determine if he should gain his trust the Buddha says, "And the Dhamma that he teaches is profound, hard to see and hard to understand, peaceful and sublime, unattainable by reasoning alone, subtle, to be experienced by the wise." What's in this passage that I've started to understand about practiced philosophy, be it Buddhist or stoic, is that talking about it alone is not enough, and reason alone is not the path to it. I mean to say that in order to really understand, it must be experienced, it has to be "seen" with ones own eyes. In this way the writing of these thinkers is more like a report from an explorer who is trying to describe the places he has been and what he has seen, but we all know that it is one thing to listen to a description of places and wholly another thing to experience them for yourself. In this way one can not just read books and gain wisdom, it's a thing that requires practice and at times guidance. It is for this reason that the Buddha asks that a student have faith in where his chosen teacher is leading them, or more accurately a sense of well founded trust.