Repentance is essential to salvation. Numerous verses verify that, including II Peter 3:9, “The Lord is not slack concerning His promise, as some count slackness, but is longsuffering toward us, not willing that any should perish but that all should come to repentance.”
Repentance when used in reference to our salvation means “to change your mind about whatever is keeping you from trusting Christ and trust Him to save you.”
For some of us, that may mean changing our minds about our good deeds and recognizing that those good works will not get us to heaven. Others must change their mind about the person of Christ and recognize that He is indeed the Son of God who died as their substitute on a cross. Still others must change their mind about sin and recognize that sin is what God calls it—sin.
When a person changes his mind about whatever is keeping him from trusting Christ and trusts Christ to save him, at that time repentance has taken place.
That is one reason repentance is often called the opposite side of the same coin. The one side says repent and the other believe.
That is also why in the Gospel of John—written to tell us how to receive eternal life (John 20:31)—98 times it tells us to believe but not once to repent. The reason being that if we believe in the Biblical sense of the word, we have repented.
We come to God as sinners, recognize, Christ died for us and rose again, and trust Christ to save us. At that point both faith and repentance have taken place.