In general repentance means change, particularly a change in a way of thinking. In the New Testament the Greek word translated as repentance (metanoia/metanoya) basically means to think differently after; as in something happens and we think differently afterward. We all go through different things and/or experience events in our lives that result in repentance, or a change in a way of thinking, that have nothing to do with Jesus or Christianity. One classic example is the idiom "fool me once, shame on you; fool me twice, shame on me." The expectation here is that we should learn from our mistakes, change our way of thinking (or repent) after being fooled once so that we (because we are now thinking differently) don't let our self be fooled again. The concept of repentance can have different connotations but my point here is that repentance is not a Christian concept; it's generic.
For Christians repentance primarily has meaning within our relationship with the Logos of God, or Jesus. In the post "Who is Jesus" I stated the original definition for Logos; the "divine reason or plan which coordinates a changing universe." Repentance for salvation starts with an awareness or understanding that our reasoning and plans are in conflict with Jesus. Basically we are wrong and He is right. Not we did something wrong, we are wrong. Next comes a willingness to die to our own reasoning and plans. And afterward faith that Jesus will work His divine plan in us.
The Apostle Paul said in Galatians 2:20 - 20I have been crucified with Christ and I no longer live, but Christ lives in me. The life I live in the body, I live by faith in the Son of God, who loved me and gave himself for me. (NIV).
This is the repentance, or way of thinking, that leads to salvation.