Right away, we think of confessing our sin before God, praying and asking for His forgiveness. Maybe this has been heard preached by the pastor on a Sunday morning, or from a friend that has shared the Gospel with another person and this is commonly what comes to mind.
The Greek word for repent is metanoeō (met-an-o-eh'-o) and it means to think differently or afterwards, that is, reconsider (morally to feel compunction).
I found the first commentary excerpt by John Gill concerning this verse on another ministry website and thought how simple and yet profound this explanation really is. I then looked at the other commentaries on my e-Sword program and found Matthew Henry's to be equally as compelling and a blessing to enhance my understanding of the text.
May this be a blessing to enrich your understanding of the Gospel and what it means to repent and believe the gospel.
"repent ye, and believe the gospel." Mark 1:15
He called them to repent, not only of their former sins and vicious course of life, but of their bad principles and tenets, concerning a temporal kingdom of the Messiah; concerning merit and free will, justification by the works of the law, and salvation by their obedience to the ceremonies of it, and the traditions of the elders: these he exhorts them to change their sentiments about, and to relinquish them, and give into the Gospel scheme; which proclaims liberty from the law, peace, pardon, and righteousness by Christ, and salvation and eternal life by the free grace of God. John Gill
By repentance we must lament and forsake our sins, and by faith we must receive the forgiveness of them. By repentance we must give glory to our Creator whom we have offended; by faith we must give glory to our Redeemer who came to save us from our sins. Both these must go together; we must not think either that reforming our lives will save us without trusting in the righteousness and grace of Christ, or that trusting in Christ will save us without the reformation of our hearts and lives. Christ hath joined these two together, and let no man think to put them asunder. They will mutually assist and befriend each other. Repentance will quicken faith, and faith will make repentance evangelical; and the sincerity of both together must be evidenced by a diligent conscientious obedience to all God's commandments. Thus the preaching of the gospel began, and thus it continues; still the call is, Repent, and believe, and live a life of repentance and a life of faith. Matthew Henry's Commentary
Meyers, R. (2006). e-Sword. The sword of the Lord with an electronic edge (Verson 7.8) [Computer software].