In its origins, the word 'repentance' has something to do with 'turning around'.
So when we repent (of our sins), we turn our back on sin and turn towards God so that we can look God in the face. And we resolve to avoid the cause of sin in the future.
Related ideas include penitence and forgiveness.
We are usually penitent (sorry for the wrong we have done) before we repent and God responds to our repentance with forgiveness.
In the sacrament of Holy Baptism, the candidates (or their godparents) say that they repent of their sins during the part of the service called 'The Decision' before the minister makes the sign of the cross on the forehead of the candidate.
© J D Yule 2003