There's a lot of confusion about what faith is. A lot of people use it to mean simply "irrational belief", or even "counter-rational belief". This is confusing because I think it's not what Christians mean when they talk about faith. More specifically, it's not what the Bible means. For example, Abraham is described as a paragon of faith, even though God appeared to him and spoke to him several times. Abraham's faith wasn't grounded in ignorance or uncertainty.
So what is it? Hebrews says
Now faith is being sure of what we hope for and certain of what we do not see.
and goes on to list "heroes of faith", including Abraham:
By faith Abraham, when called to go to a place he would later receive as his inheritance, obeyed and went, even though he did not know where he was going. By faith he made his home in the promised land like a stranger in a foreign country; he lived in tents, as did Isaac and Jacob, who were heirs with him of the same promise. For he was looking forward to the city with foundations, whose architect and builder is God.Then later
They did not receive the things promised; they only saw them and welcomed them from a distance.
What Abraham "hoped for" and "did not see" was not the existence of God himself, but the eventual fulfillment of God's promises to him. That's what his faith was about.
Why is that commendable? If Abraham had been some kind of Mesopotamian Vulcan, logic would dictate that after God appeared to him the first time, following God's instructions would be the only reasonable course of action forever after. But of course it doesn't work like that for anyone, because we're all weak. Everyone, Christian or not, has times when we clearly know what we should do but simply lose heart and capitulate. For Christians, this means that we simply don't trust God enough. We may intellectually be convinced that he exists, that he loves us, and all that good stuff, but we effectively decide in our hearts "I'd better take my pleasure now because I'm not sure obeying God is a net win".
Faith isn't just something we have in relation to God either. I'm firmly convinced that working on Firefox is the right thing for me to be doing, but sometimes I don't feel it, and I'm tempted to skive off and spend time on something else. I honestly profess that everyone will be happier in the long run if I am a good husband and father, but there's always a temptation to be a selfish beast, even in situations where I know that it's going to hurt me in the long run. I need faith in my original convictions in order to get me through those temptations, to live in light of that unseen reward, whatever it may be. This faith is more about trust and loyalty than "mere belief". Ironically, in this sense faith is particularly rational.