What does the Bible mean by grace?
Someone summarized the biblical doctrine of grace as:
GRACE: God's Riches At Christ's Expense.
The New Testament word charis is most often translated "grace," especially meaning God's gift of salvation in Christ.
It is because of Christ's death for us that a holy God is able to exercise grace toward us and remain righteous in doing so.
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How is grace different from mercy? It was God's love and mercy that moved Him with compassion to provide a Savior for us. But God could not save us just on the basis of compassion alone! A price had to be paid.
We receive by faith God's Riches At Christ's Expense:
4 But because of his great love for us, God, who is rich in mercy, 5 made us alive with Christ even when we were dead in transgressions—it is by grace you have been saved (Ephesians 2:4-5).
It is a gift, not something we derserve or can ever earn by good works,
8 For it is by grace you have been saved, through faith—and this is not from yourselves, it is the gift of God— 9 not by works, so that no one can boast.