Faith is a word with many meanings. It can mean faithfulness.
It can mean absolute trust, as shown by some of the people who came to Jesus for healing (Luke 7:2-10). It can mean confident hope (Hebrews 11:1). Or, as James points out, it can even mean a barren belief that does not result in good deeds (James 2:14-26). What does Paul mean when, in Romans, he speaks of saving faith?

We must be very careful to understand faith as Paul uses the word, because he ties faith so closely to salvation. It is not something we must do in order to earn Salvation--if that were true, then faith would be just one more deed, and Paul clearly states that human deeds can never save us (Galatians 2:16). Instead, faith is a gift God gives us because he is saving us (Ephesians 2:8). It is God's grace, not our faith, that saves us. In his mercy, however, when he saves us he gives us faith--a relationship with his Son that helps us become like him. Through the faith he gives us, he carries us from death into life (John 5:24).

Even in Old Testament times, grace, not deeds, was the basis of salvation. As Hebrews points out, "It is impossible for the blood of bulls and goats to take away sins" (10:4). God intended for his people to look beyond the animal sacrifices to him, but all too often they, instead, put their confidence in fulfilling the requirements of the law--that is, performing the required sacrifices. When Jesus triumphed over death, he cancelled the charges against us and opened the way to the Father (Collossians 2:12-15). Because he is merciful, he offers us faith. How tragic if we turn faith into a deed and try to develop it on our own! We can never come to God through our own faith, any more than his Old Testament people could come through their own sacrifices. Instead, we must accept his gracious offer with thanksgiving and allow him to plant the seed of faith within us.
Life Application Study Bible, Zondervan