This has been a popular subject over the years, but I have adopted a definition of faith as 'right response to grace' or 'right response to revelation'. I think we see this definition at work all throughout the scriptures. What I am about to write is not a standard definition that can be found in any theological books that I am aware of, so it has to stand on its own feet with few assumptions being made.
But they have not all obeyed the gospel. For Isaiah said, Lord, who hath believed our report? So then faith comes by hearing, and hearing by the word of God. (Romans 10:16-17 KJV)
Our passage sheds light on an age old question as to where faith originates. Some have wondered where Abraham got his faith. Did he and others like him somehow reach inside themselves and 'self-generate faith'? Did God simply give them faith? Based upon a careful reading of our text the answer is clearly no. Faith has two components: revelation and right response. (see Hebrews 4:2) God initiates the process of the generation of faith by revealing His word to a person. Faith cometh by hearing. This has always been how faith 'comes'. God's word contains within itself the grace (divine enabling) needed to accomplish what God has said. It is no more complicated than that. God has enabled everyone that hears His word to believe no matter how depraved they may be. Even a reprobate can and must obey God when they receive revelation of His will. In fact, when God speaks the dead can come forth from a grave. Men can walk on water when God speaks to them to do so. This is the key factor. Faith cometh by hearing and hearing by the Word of God. How can this be. We have another clue in Luke 1:26-38)
And, behold, thy cousin Elisabeth, she hath also conceived a son in her old age: and this is the sixth month with her, who was called barren. For with God nothing shall be impossible. And Mary said, Behold the handmaid of the Lord; be it unto me according to thy word. And the angel departed from her. (Luke 1:36-38)
Notice in our text that in Luke 1:37 we have the KJV English rendering, For with God nothing shall be impossible. Most all mainstream translations follow this rendering in so much that it is a common line quoted in Christmas stories and plays thousands of times each December. The statement is true, but it is NOT what the text actually says. If the translators had been a bit more pedantic the whole of Christendom could have had a better understanding of what faith actually is. But there it is. The American Standard Version gets it right; for no word from God shall be void of power.
Observe again, the Greek text reads, ὅτι οὐκ ἀδυνατήσει παρὰ τῷ Θεῷ πᾶν ῥῆμα (Luke 1:37). Here we have ῥῆμα (rhema), word, as distinguished from λόγος (logos), word, in classical Greek, signifies a constituent part (essential part) of a speech or writing, as distinguished from the contents as a whole. Thus it may be either a word or a saying. Sometimes a phrase, as opposed to ὄνομα, a single word. The distinction in the New Testament is not sharp throughout. It is maintained that ῥῆμα in the New Testament, like the Hebrew דָּבַר, stands sometimes for the subject matter of the word; the thing, as in this passage. But there are only two other passages in the New Testament where this meaning is at all admissible, though the word occurs seventy times. These are Luke 2:15; Acts 5:32. “Kept all these things” (Luke 2:19), should clearly be sayings, as the KJV itself has rendered it in the almost identical passage, verse 51. In Acts 5:32, Rev. gives sayings in margin. In Luke 2:15, though KJV and Rev. render thing, the sense is evidently saying, as appears both from the connection with the angelic message and from the following words, which has come to pass: the saying which has become a fact. The Rev. rendering of this passage is, therefore, right, though a little stilted: No word of God shall be void of power; for the KJV errs in joining οὐκ and πᾶν, not every, and translating nothing. The two do not belong together.
The statement is, Every (πᾶν) word of God shall not (οὐκ) be powerless. The KJV also follows the reading, παρὰ τῷ Θεῷ, with God; but all the later texts read παρὰ τοῦ Θεοῦ, from God, which fixes the meaning beyond question. (Vincent) It is odd that the translators then translate the same word ῥῆμα as 'word' when Mary replied, 'be it unto me according to thy word.' The translators variety of words has caused the masses of English readers to miss the precious link between Verse 37 and 38. Unfortunately the new translations still do not correct this as we see in the NASB, NKJV, NIV and ESV.
So we see then that NO WORD from God shall be void of power, that is, the grace required to accomplish it. When God speaks to us we can do what He is saying to do. How we respond to Him speaking is either faith (right response) or sin (wrong response). A grat many things are impossible until God speaks. That is the key. God has to speak to our hearts bringing revelation of His will. when this happens we can and must respond 'rightly'. Here are some examples of how Jesus spoke and the impossible bacame possible.
1. And looking round about upon them all, he said unto the man, Stretch forth thy hand. And he did so: and his hand was restored whole as the other. (Luke 6:10)
This man could not stretch forth his hand as it was withered until Jesus spoke. His very word enabled the impossible.
2. When Jesus saw him lie, and knew that he had been now a long time in that case, he saith unto him, Wilt thou be made whole?
The impotent man answered him, Sir, I have no man, when the water is troubled, to put me into the pool: but while I am coming, another steppeth down before me.
Jesus saith unto him, Rise, take up thy bed, and walk.
And immediately the man was made whole, and took up his bed, and walked: and on the same day was the sabbath. (John 5:6-9)
Observe that the man was a long time unable to rise from his bed. Jesus spoke the words, Rise, take up thy bed, and walk. The grace necessary to fulfill the command was resident in the words.
3. Saying, What wilt thou that I shall do unto thee? And he said, Lord, that I may receive my sight.
And Jesus said unto him, Receive thy sight: thy faith hath saved thee.
And immediately he received his sight, and followed him, glorifying God: and all the people, when they saw it, gave praise unto God. (Luke 18:41-43)
Here is a man that by implication had 'heard' about Jesus. He cried out in faith. Jesus spoke the words, 'Receive thy sight'. The man immediately received because he was prepared to mix faith (right response to revelation) with the words spoken. It was only God's grace that He spoke. But when He speaks we are enabled by the grace empowerd revelation (the Word of His grace) to do what He said. Blessings.