Religion

I suspect ya'll be talkin' 'bout faith more than belief.

In my industry, where we design and build things that have never existed before. We "believe" we can do it. Admittedly, we've done it so often it isn't always that huge leap of "faith". Every couple of decades or so we fail miserably (although that usually means we just change the requirements as oppose to giving up). Belief can be important too in emergency situations. Believing that one will survive, that help will come, that there is a way out. That former monk in the cave with those kids needed alot of belief to keep them alive and get them out. Was that all he needed? No, but it was an important element.

Faith on the other hand is in essence the belief in things that aren't evident, and to some degree never will be.