Martin Luther and John Calvin are some of the well-known theologians of the Christian faith. Both of them have written about what faith is:

"Where there is the Word of the God who makes promises, there must necessarily be the faith of the person who accepts those promises. It is clear that the beginning of our salvation is a faith which clings to the Word of a promising God who, without any effort on our part, in free and unmerited mercy goes before us and offers us a word of promise." --Martin Luther, The Babylonian Captivity of the Church (The essay against the corruptions of the Roman Catholic Church)

"Now we shall have a right definition of faith if we say that it is a steady and certain knowledge of the divine benevolence towards us, which is founded upon the truth of the gracious promise of God in Christ, and is both revealed to our minds and sealed in our hearts by the Holy Spirit." --John Calvin, Institutes of the Christian Religion (Basically a systematic theology book)

From this, Luther talked about 3 things about faith:
1. Faith has a personal, rather than a purely historical, reference. (Not simply historical knowledge.)
2. Faith concerns trust in the promises of God.
3. Faith unites the believer to Christ.

Calvin talked about a few things about faith:
1. "a steady and certain knowledge"
2. "Knowledge of the divine benevolence towards us" (Not just about God, but God's goodness)
3. involves both heart and mind. Affects both.
4. "founded upon the truth of the gracious promises of God in Christ" (Based on God's promises; grounded on truth, not a human invention or delusion.)
5. Trinitarian: All parts of the trinity is involved in the aspect of faith.

(Quotes and points taken from Theology: The Basics, by Alister E. McGrath)

Faith is an active belief in what you do not see. Faith is a very deep and personal trust in something really.

Those are some good points to put thought into. Personally, I think faith, in Christianity, is putting your complete trust in the "logical-unknown", and then because of it have your life turned upside down. Then if you recognize your state as because of your commitment, you can continue that complete trust in an outcome according to God.

Not only this, but when you experience the outcome, it's a blessing beyond imagination. So I think you can either view faith as an oxymoron, as hyperbole, or you can experience it as a reality.

The Bible its self tells what faith is. It is found at Hebrews 11:1 Here is the KJV

KJV Hebrews 11:1 Now faith is the substance of things hoped for, the evidence of things not seen.

So faith really is a belief in the promises of God. But not a blind belief but belief based on evidence. Another Translation puts Hebrews 11:1 this way which makes it easier to understad

Hebrews 11:1 Faith is the assured expectation of things hoped for, the evident demonstration of realities though not beheld.

But was Evidence or Evident demonstrations do we have to base or belief in Gods promises?

Well there are scores and scores of prophecy in the bible detailing many things. And all of the ones that has been written down in the bible have come turn all the way up to our time. Take two for an example. First one. God stated he would allow the Babylonians to destroy the Jews and then 70 years later they would be release (this was written down many many decades in advance by both Isaiah and Jeremiah) the release would come from babylon being over throw by a king names Cyrus he would do this by diverting the river away from the city and take the city unchallenged according to the bible, did this happen? YES! Archeological records support it in its exact detail. Even to the name of the king Cyrus. Second (In the book of Daniel)the bible states that a Goat with a large horn would strike down a ram the bible points to the rame being Medo-Persia the Goat the bible states is the king of Greece and once the ram struck medo-Persia and conquered the then known world the large horn would be broken and 4 would grow in place of it, but not with its power. Did this happen? YES Greece beat Medo-Persia in warfare the person? Alexander The Great! What happen after he conquered the then known world? He Died! And his 4 Generals ruled in place of him but never with his strength and power! That is a part of the evidence but there is so much more. All things foretold to take place in the past took place so those who have studied such evidence have faith that the rest of the bibles prophecy will come true like all the rest have.