My working definition of faith, which is borrowed verbatim from Sharon Salzburg, a Buddhist writer and teacher, in her amazing book Faith: Trusting Your Own Deepest Experience:

"Faith does not require a belief system, and is not necessarily connected to a deity or God, though it doesn't deny one. This faith is not a commodity that we have or don't have-- it is an inner quality that unfolds as we learn to trust our own deepest experience.... No matter what we encounter in life, it is faith that enables us to try again, to trust again, to love again. Even in times of immense suffering, it is faith that enables us to relate to the present moment in such a way that we can go on, we can move forward, instead of becoming lost in resignation or despair. Faith links our present-day expereince, whether wonderful or terrible, to the underlying pulse of life itself." (I could also have just excerpted the entire book here, but that would be a bit impractical.)