Hebrews 6:1-3 tells us to have 'faith towards God'. From this instruction we can understand that people often have faith towards something other than God, or faith from something other than God.
In street language of newspapers and magazines, the word faith is thrown around loosely to include faith towards all kinds of things. Therefore some distinction becomes necessary to explain. I hope this clears up the definition for you.

A man can have some other kind of faith, such as when the banker calls and says, come on down and get your money, we tend to believe the banker and have confidence that when we go we will be getting the money. That is faith in what the banker said. God tells us to have the faith of God, that is to have faith by what God says. Then as we believe what God says, we shall also see His word come to pass. His word does not return void. His word is the good seed.

Faith towards God is the living faith defined in Hebrews 11:1-3. There are also dead works produced by dead faith. Examples of dead faith include imaginations, and doctrines of devils, etc. Countless kinds of faiths and mixtures of faith are possible. That's why in Hebrews 6 we read, the phrase specifying "repentance from dead works and faith towards God...".