What Faith Is
When I graduated from Christian high school after spending my entire life being brought up in church, I'm not sure I could have put into words what it meant to "have faith". Not that I didn't have it myself; I'd been a believer since the ripe old age of seven. But I don't think I could've adequately described to you what faith was or what it meant to have it. Pondering the situation now, I'm fairly certain that many Christians are in the same boat.
Seeing how often we Christians find ourselves at a loss when actually asked about the things we talk about all the time (and that it is a supremely important part of Christianity to begin with), it seems incumbent and vital to come up with an appropriate working definition of what the Bible means by “faith”. And while “faith" is certainly a loaded term that carries an understandable amount of weight, the actual concept behind it is not hard at all.
In a phrase, faith can probably best be defined as "risk-taking". A more technical and philosophical description that's been passed down to me is, "commitment without knowledge". It is stepping out into the void without knowing what, if anything, will catch you (think of Indiana Jones’ final test before reaching the grail chamber in The Last Crusade). The words "trust" and "believe" are the verb forms; to trust or believe someone is to have faith in them. It is more than just mental acknowledgment or understanding: faith affects one's behavior and alters the course they would have otherwise chosen.
So, given this basic definition of faith, one begins to see what it means to actually have it in the Christian sense. Simply, to have faith in God is to believe Him - when He says that He loves us (Romans 5:8), that He will judge all of us after death (Hebrews 9:27), that He will punish sin (Matthew 25:41) and reward righteousness (Matthew 25:34), for example. It also means that the totality of one's hope for a positive outcome to life resides not within the self, but in the sacrifice of Christ on their behalf (Acts 16:31): we look to Christ and not ourselves as our sole hope for salvation.
So, essentially, the Christian bets every last chip in his hand on God. He goes all-in on the testimony and revelation of Scripture. He rejects the natural human inclination for self-reliance and cedes control to something he cannot prove in a naturalistic sense. Faith resides beyond the bounds of empirical knowledge. This is how God designed it to be (Hebrews 11:1) and it stands as the prerequisite to all other positive, familial interaction with Him (Hebrews 11:6).
A couple of simple observations…
First, the kind of faith that Christians advocate is both essential and transformative. God requires an uncertain (that is, unprovable) commitment from us before He permits us to consider ourselves a legitimate part of His family (John 1:12; I John 3:1). And the kind of commitment that believes what He has said in holy scripture must, by definition, cause behavioral, spiritual, and philosophical change (coincidentally, all of this is why it is a fundamentally un-Christian idea to suggest that all people everywhere are God’s children). Mental acknowledgement of the reality of God and the truthfulness of His claims is not enough because it's not really faith. If someone wants to be sure that they actually believe they must make sure that they're actually changing (Matthew 3:8; II Peter 1:4-8; II Corinthians 7:10-11; Ephesians 5:8-9). Or, to put it more simply, if God has told you that you will regret for all eternity a lifetime of sinful debauchery and self-centeredness (and He has), then a real trust in Him will necessarily cause you to change your ways. If God has told you that a new world is coming in which you are meant to live, work, and flourish, then having faith in Him means living like you believe this future promise to be a sure thing and preparing for it properly (I Peter 2:9; II Peter 3:13; Isaiah 65:17).
A less obvious observation is this: everyone everywhere lives by faith. There is no one in this world who does not commit to things without knowing what the ultimate outcomes of their choices will be. The question is not really whether or not you have faith. The question is what the object of your faith happens to be: what are you placing your faith in? Even the most hardened, militant atheist walks in some way by faith. If he doesn't believe you when you inform him of this fact, just ask him to empirically prove how he can know for certain that his wife loves him or that his flight next week to Duluth will land safely. We all commit to things we cannot know everything about when the commitment is initially made: we may have plenty of circumstantial evidence and testimony that we trust but those things are not the same as certainty, which is knowledge beyond-the-shadow-of-a-doubt.
Faith, the commitment without total knowledge, is the system God built by which He most wanted to be known. (In this life, at least.) Similar to how we trust a plane and a pilot to get us safely to our destination, Christians trust Yahweh to deliver on the promises He has made in Scripture.
The old axiom says that, "Seeing is believing.” But God flips this truism on its head (II Corinthians 5:7 says, "[W]e walk by faith, not by sight.”). To know God, we must have faith in Him. And to have faith in Him is to believe what He says in His Word and to trust that His sacrifice on the cross is enough to achieve for us what He has promised.
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And without faith it is impossible to please Him, for whoever would draw near to God must believe that He exists and that He rewards those who seek Him. – Hebrews 11:6
For you have need of endurance, so that when you have done the will of God you may receive what is promised. For, “Yet a little while, and the coming one will come and will not delay; but my righteous one shall live by faith, and if he shrinks back, my soul has no pleasure in him.”
But we are not of those who shrink back and are destroyed, but of those who have faith and preserve their souls. – Hebrews 10:36-39
Then he brought them out and said, “Sirs, what must I do to be saved?” And they said, “Believe in the Lord Jesus, and you will be saved, you and your household.” – Acts 16:30-31
Further discussion here:
Absolute certainty is the antithesis of faith. Knowing something beyond the shadow of a doubt negates your ability to have faith in it. And, since faith is necessary to please God (Hebrews 11:6), Christians can know that absolute certainty of the reality of God and the veracity of His promises is not the goal of faith.