My favorite explanation and demonstration of faith is Jesus' encounter with the Roman centurion.

"And when Jesus was entered into Capernaum, there came unto him a centurion, beseeching him, and saying, Lord, my servant lieth at home sick of the palsy, grievously tormented. And Jesus saith unto him, I will come and heal him. The centurion answered and said, Lord, I am not worthy that thou shouldest come under my roof: but speak the word only, and my servant shall be healed. For I am a man under authority, having soldiers under me: and I say to this man, Go, and he goeth; and to another, Come, and he cometh; and to my servant, Do this, and he doeth it. When Jesus heard it, he marvelled, and said to them that followed, Verily I say unto you, I have not found so great faith, no, not in Israel." Matthew 8:5-10.

From this, it can be seen that faith is not simply a matter of believing the word, but relying on the word to accomplish that which the word says in contrast to our attempts to bring the word to pass through our own endeavors.