The Greek word metanoeo, the verb form of the noun metanoia, translated "repentance," means "to perceive afterwards." It always has to do with a person realizing their perspective was wrong, resulting in a humble change of mind. Repenting, or having a change of mind, is an extremely important part of a person's salvation experience. When Jesus was giving His disciples instructions on what they were to preach, He listed repentance first and remission of sins last (Lk. 24:47). Just to show how important repentance is, "remission of sin" is the finished work of Jesus on our behalf, and is based upon His death, burial, and resurrection; it is the Gospel (1 Cor. 15:1-4). Because the Gospel is the power of God unto salvation, having listed repentance first means it is obviously of extreme importance (Rom. 1:16).
When I think of what it means to truly repent, I like to picture a man walking away from God, with his eyes focused upon the world, and having no concern for a relationship with the Father. God calls out his name, trying to get him to turn and come to Him (Jn. 6:44). Repentance is when he realizes his mistake and turns around with a desire to submit. The salvation experiences in the Bible show how men had changed their minds about letting God be their God (Acts 9:1-6; 16:27-34). In fact, Paul heard the voice of Jesus and immediately had a change of heart and mind. In the case of the Philippian jailer, he went from being suicidal, to being hospitable.
It is unfortunate that the word "repent" is so misunderstood. The vast majority of people think of it in religious terms meaning to "turn over a new leaf," or to stop speaking and acting improperly. Even the lost have a conscience, and if they haven't seared it so badly that it does not function, they feel guilt and remorse (1 Tim. 4:2). While a conscience tends to cause man to agree with religious teachings, and often make a commitment to change his ways, it is neither permanent, nor necessarily associated with a life of submission to the will of God. In 2 Corinthians 7:10, two kinds of repentance are presented: one is the repentance of the lost world, which produces sorrow but no submission, and the other which produces the change of heart and mind necessary for salvation.
Genuine repentance that leads to salvation always produces a change in a person's lifestyle. We become a new person (2 Cor. 5:17). We have works that demonstrate our allegiance to God (Acts 26:20; Eph. 2:10). Our works are described as "fruit," the evidence by which others can identify us as children of God, just as the "fruits" of the lost identify them (Matt. 7:20; 13:23; Jn. 15:1-8). According to John 15:8, it is our "fruit" that produces glory for the Father. So, what is the "fruit" which results from repentance and salvation? It is the fruit of the Spirit of God Who produces it in us (Gal. 5:22-23). Truly born-again Christians, when they are walking in the Spirit, produce the fruit that wins the lost and glorifies the Father. When they are not, they need to read 1 John 1:9 and repent!
It is simply common sense that when one hears about how much he is loved of God, and understands that he is totally lost without having a relationship with the Father by trusting in the finished work of Jesus on his behalf, that he want more than anything to please Him. That is repentance!