Q: What is repentance unto life?
A: Repentance unto life is a saving grace, whereby a sinner, out of a true sense of his sin, and apprehension of the mercy of God in Christ, doth, with grief and hatred of his sin, turn from it unto God, with full purpose of, and endeavour after, new obedience.

Acts 11:18. When they heard these things, they held their peace, and glorified God, saying, Then hath God also to the Gentiles granted repentance unto life.
Acts 2:37-38. Now when they heard this, they were pricked in their heart, and said unto Peter and to the rest of the apostles, Men and brethren, what shall we do? Then Peter said unto them, Repent, and be baptized every one of you in the name of Jesus Christ for the remission of sins, and ye shall receive the gift of the Holy Ghost.
Joel 2:13. And rend your heart, and not your garments, and turn unto the Lord your God: for he is gracious and merciful, slow to anger, and of great kindness, and repenteth him of the evil.
Jeremiah 31:18-19. I have surely heard Ephraim bemoaning himself thus; Thou hast chastised me, and I was chastised, as a bullock unaccustomed to the yoke: turn thou me, and I shall be turned; for thou art the Lord my God. Surely after that I was turned, I repented; and after that I was instructed, I smote upon my thigh: I was ashamed, yea, even confounded, because I did bear the reproach of my youth.
2 Corinthians 7:11. For behold this selfsame thing, that ye sorrowed after a godly sort, what carefulness it wrought in you, yea, what clearing of yourselves, yea, what indignation, yea, whatfear, yea, what vehement desire, yea, what zeal, yea, what revenge! In all things ye have approved yourselves to be clear in this matter.
Psalm 119:59. I thought on my ways, and turned my feet unto thy testimonies.

Westminster Project - See Thomas Watson's Body of Divinity on Repentance in the WSC