I have an atheist friend, Anthony, who does interviews on college campuses, asking students about their religious beliefs. He skillfully engages in Socratic dialogue, asking them about why they believe what they do and helping them identify flaws in their reasoning. When people mention “faith,” he frequently asks a question like this, “Do you think faith is a reliable way of coming to know things?” Anthony thinks of faith as a “way of knowing” in contrast to other ways, like science. Science uses evidence derived from observation, experimentation, etc. to test new ideas, where as the “faith-way” simply uses feelings, intuitions or positive-thinking; evidence need not apply. Put this way, science and faith are two radically different, and somewhat opposed, approaches to discovering truth.
Is this really what faith is? Ask ten religious believers what faith is, and you’ll get twelve definitions. Certainly one (or more) of them will sound a lot like what Anthony hears in his interviews. But taking polls isn’t the best way to determine truth. Defining (Christian) faith should start with the Bible and the great minds who have written on this over the centuries. But rather than launch into a survey of these sources, I’ll offer my best take based on my own study of them:
Faith is trusting in what you have good reason to believe is true. 
For example, I’ve done “trust falls” with others on a number of occasions. Usually, they work like this. You are told that persons X and Y will stand behind you and catch you when you fall backward. You know persons X and Y well enough — they are reliable and strong enough to catch you. They’re clearly right behind you. But then you face forward with arms crossed, and you struggle to force yourself to fall freely backward. You can’t see their arms extending to catch you. Your instinct of self-protection shouts, “Don’t fall backward! You’ll hurt yourself!” But you have every reason to rationally believe that you won’t crack your skull on the floor. If someone asked you, “Do you believe they will catch you?” you would most likely answer, “Yes.” But trusting means letting yourself fall. This illustrates faith very well.
Faith On Level Ground
So given this definition, is faith somehow inferior to science? I don’t think so. First off, on this view, faith isn’t a way of knowing, it is a way of living. Trusting is a behavior–a behavior based on what you believe. I don’t come to know things “by faith,” I live “by faith.” Faith without works is dead, as St. James says. This understanding of faith follows the narrative of the New Testament much more closely.
Second, faith and science actually share some significant qualities. Scientists base beliefs on good reasons. Moreover, they often place their trust in those beliefs. A chemist in a lab believes that mixing certain chemicals will produce a certain reaction. Furthermore, she trusts that her equipment is safe and reliable–she willingly mixes the chemicals. An astronomer believes the stars and planets are in such-and-such a position because he has seen it through his telescope. And he demonstrates trust in his equipment and findings by publishing them in a journal. Scientists trust the process of scientific inquiry, meaning that they believe, for good reasons, that it is reliable, and they demonstrate this trust by using the process and acting according to their findings. So, scientists employ “faith” in much the same way that Christians do, on my view.
No doubt, some of you will object to my definition of faith and insist that faith must be essentially irrational, which fits more comfortably into your narrative of “faith against science.” Or some may argue that faith is some kind of spiritual phenomenon, divorced from the process of reason, and cannot be compared to scientific knowledge. But I hope most can see the logic and elegance of what I have proposed.
If I’m right, or close to right, about the nature of Christian faith, then there’s no reason to think that science stands in a superior position, epistemically or in any other sense. Belief in God and belief in quantum particles come about in much the same way, even if the kinds of evidence are different. Faith in God, however, may be special in that it is not merely the result of a human decision to trust. Some theologians think that we can’t overcome our reluctance to take that “trust fall” with God without Supernatural assistance. In this sense, it may be superior to the “faith” of science, which is merely the product of fallible human reason and psychology.
 Hebrews 11:1 is the classic passage, and I like the Latin translation: “est autem fides sperandorum substantia rerum argumentum non parentum.” The Latin uses the term ‘argumentum’ to suggest that faith is that which persuades us of what we cannot perceive with our senses, or as Thayer’s Greek lexicon puts it, “that by which invisible things are proved.” This is reminiscent of science–it is how human beings discovered things like atoms and otherwise invisible celestial bodies.