While on trial before King Agrippa, the apostle Paul recounted the events surrounding his conversion to Christianity.  While doing so, he said to him:

Acts 26:19-20 (ESV)
¹⁹ “Therefore, O King Agrippa, I was not disobedient to the heavenly vision,
²⁰ but declared first to those in Damascus, then in Jerusalem and throughout all the region of Judea, and also to the Gentiles, that they should repent and turn to God, performing deeds in keeping with their repentance.

John the Baptist said something similar:

Matthew 3:7-8 (ESV)
⁷ But when he saw many of the Pharisees and Sadducees coming to his baptism, he said to them, “You brood of vipers! Who warned you to flee from the wrath to come?
⁸ Bear fruit in keeping with repentance.

Luke 3:7-8 (ESV)
⁷ He said therefore to the crowds that came out to be baptized by him, “You brood of vipers! Who warned you to flee from the wrath to come?
⁸ Bear fruits in keeping with repentance. And do not begin to say to yourselves, ‘We have Abraham as our father.’ For I tell you, God is able from these stones to raise up children for Abraham.

What does it mean to “bear fruit in keeping with repentance” and “perform deeds in keeping with repentance”?

Repentance is necessary for salvation, and as such it is a vital component of the gospel message.

Luke 24:45-47 (ESV)
⁴⁵ Then he opened their minds to understand the Scriptures,
⁴⁶ and said to them, “Thus it is written, that the Christ should suffer and on the third day rise from the dead,
⁴⁷ and that repentance and forgiveness of sins should be proclaimed in his name to all nations, beginning from Jerusalem.

Acts 3:18-20 (ESV)
¹⁸ But what God foretold by the mouth of all the prophets, that his Christ would suffer, he thus fulfilled.
¹⁹ Repent therefore, and turn again, that your sins may be blotted out,
²⁰ that times of refreshing may come from the presence of the Lord, and that he may send the Christ appointed for you, Jesus.

Acts 17:30-31 (ESV)
³⁰ The times of ignorance God overlooked, but now he commands all people everywhere to repent,
³¹ because he has fixed a day on which he will judge the world in righteousness by a man whom he has appointed; and of this he has given assurance to all by raising him from the dead.

To repent (metanoeo) literally means “to change one’s mind; to think differently or afterwards, i.e. reconsider…”  To use a non-religious analogy for clarification, say you and a friend are looking for a place to eat lunch.  You say, “What do you think about Taco Bell?”  Your friend says, “Sounds good, let’s go,” and so you both are on your way to the nearest Taco Bell.  Yet two blocks from Taco Bell you see a Chick-Fil-A and your friend says, “Hey, there’s Chick-Fil-A!  I could eat me some waffle fries!”  And you say, “Yeah, I’m in the mood for a chicken sandwich!”  So you pull into Chick-Fil-A instead of continuing on to Taco Bell.  What did you do?  You both changed your minds about Taco Bell, resulting in your actions turning you away from Taco Bell and towards what your minds were now set upon: Chick-Fil-A.  Thus, one could say that you repented of Taco Bell.

In like manner, when we repent of our sins, that means we’ve changed our minds about our sins.  How?  Consider what Paul said:

2 Corinthians 7:9-11 (ESV)
⁹ As it is, I rejoice, not because you were grieved, but because you were grieved into repenting. For you felt a godly grief, so that you suffered no loss through us.
¹⁰ For godly grief produces a repentance that leads to salvation without regret, whereas worldly grief produces death.
¹¹ For see what earnestness this godly grief has produced in you, but also what eagerness to clear yourselves, what indignation, what fear, what longing, what zeal, what punishment! At every point you have proved yourselves innocent in the matter.

What produces repentance that leads to salvation?  “Godly grief” or “godly sorrow” over one’s sins.  Not worldly sorrow over our sins, but godly sorrow.  Worldly sorrow over sin is comparable to the thief who isn’t sorry he stole, but is terribly sorry he’s going to jail.  Godly sorrow would have the thief, regardless of whether he’s caught, truly sorrowful that he stole in the first place.  That’s because he feels the same kind of sorrow and grief over his sins that God feels.  That is what motivated him to change his mind about his sins, i.e., repent of his sins.  One gets this godly grief or sorrow over their sins when they contemplate with gratitude the kindness and patience of God (Rom. 2:4; 2 Pet. 3:9), as well as His wrath and fury concerning sin (Rom. 2:5-11).

Furthermore, take note of 2 Corinthians 7:11 again.  Notice what the verse says this “godly grief has produced in you.”  This brings us to a better understanding of exactly what it means to “bear fruit in keeping with repentance” and “perform deeds in keeping with repentance.”

Paul first mentions “earnestness,” i.e., zeal, being passionate to do what is right.  He then speaks of having an “eagerness to clear yourselves,” i.e., being eager to absolve yourself of blame, being quick to stop doing what is wrong.  He then mentions “indignation,” which would consist of having anger and moral outrage towards the sin you committed which required you to repent of it.

Paul then spoke of “fear,” specifically fear of repeating the sin, fear that the sin would not be entirely removed from you, fear of God’s punishment (cf. Acts 2:36-37).  He also talked of “longing,” a vehement, passionate desire to be right in the sight of God.  He then spoke of “zeal,” an eager and ardent pursuit of what is right, working hard to turn from the sin and become what God wants you to be.

The apostle then mentioned “punishment,” which refers to having a willingness to see justice done, even if it means taking whatever consequences must come from the sin you’ve committed.  He then closed by saying, “At every point you have proved yourselves innocent…”, showing that repentance is not half-hearted or done out of apathy; rather, it requires 100% commitment.

These traits are what true repentance requires.  They are the “fruit” one shows when one has truly repented, the “deeds” one does which are “in keeping with repentance.”  Have you repented of your sins and submitted to baptism in Jesus’ name to receive forgiveness?

Acts 2:36-41 (ESV)
³⁶ Let all the house of Israel therefore know for certain that God has made him both Lord and Christ, this Jesus whom you crucified.”
³⁷ Now when they heard this they were cut to the heart, and said to Peter and the rest of the apostles, “Brothers, what shall we do?”
³⁸ And Peter said to them, “Repent and be baptized every one of you in the name of Jesus Christ for the forgiveness of your sins, and you will receive the gift of the Holy Spirit.
³⁹ For the promise is for you and for your children and for all who are far off, everyone whom the Lord our God calls to himself.”
⁴⁰ And with many other words he bore witness and continued to exhort them, saying, “Save yourselves from this crooked generation.”
⁴¹ So those who received his word were baptized, and there were added that day about three thousand souls.