Mark Twain supposedly said "Faith is believin' what you know ain't so." Peter Boghossian, in "A Manual for Creating Atheists," insists that faith is pretending to know things that you don't know. And he insists that other definitions of faith, for example faith in a person's ability to do something, are not really faith, because they're based on your knowledge of the person's ability and history. I think he's wrong to say that this definition of the word is invalid, because it's certainly how it's used most of the time. What he's trying to do is get people to see that that sort of faith does not equal faith in the Biblical sense. That's true -- it's a different thing, and perhaps it gives people who have religious faith (belief in gods and spirits and miracles) some reason to think that their faith is reasonable, because the same word has a meaning that reflects faith justified by evidence.
But what does the Bible actually say? Well, most everyone has heard the verse: Hebrews 11:1 -- "Now faith is the substance of things hoped for, the evidence of things not seen." Christians (and many non-Christians) can quote this off the top of their heads. But what does it actually mean? It is the Biblical definition of faith. What is it getting at?
This verse begins the passage often referred to as the "Hall of Faith." The Hebrew writer goes on to talk about what certain Old Testament heroes did because they had faith. Generally speaking, the point is that they couldn't see the future things that their god had promised them, but they believed it anyway, and acted accordingly. The story of Joseph is that on his deathbed he gave instructions that when Israel would leave Egypt, they should take his bones with them to the land of promise. They weren't even in captivity yet. There weren't enough of them to be a nation yet. But he believed that his descendants would eventually go to the land that their god had promised them, and he wanted to be buried there.
So let's break that definition down. "The substance of things hoped for." If you're hoping for something but you don't have it, have never seen it, and nobody has ever seen it, then there is no "substance" to it. Faith takes the place of substance, allowing the believer to, well, believe. "The evidence of things not seen." This is essentially redundant. What is evidence? Evidence is the set of facts, observations about either physical specimens or the leftover effects of physical processes, that lead one to believe a certain thing exists, or a certain event happened. But "evidence of things not seen" implies belief without what would normally lead to belief.
To put it more succinctly, faith is a substitute for substance, and a substitute for evidence. So Boghossian's definition fits the Bible definition here. Twain, of course, was jesting. People don't know that what they have faith in isn't really so, but his statement is a way to call attention to the fact that Biblical faith allows people to believe things that they can't possibly know, and, in fact, to believe things that are demonstrably false. There's no dome above the Earth, as early Bible passages describe. The Universe is 13.8 billion years old, not the 6000-10000 you would calculate using the Bible, and it has been proven beyond a reasonable doubt.
The Hebrew writer was trying to assure his readers that there is an afterlife. There's no evidence for this at all, so in order to believe it one must accept that the New Testament writers knew it to be true. Yet the Hebrew writer himself has no confidence other than faith -- he substitutes faith for evidence, and even tells us that's what he's doing. Not very confidence inspiring, is it?