In reality, however, repenting is something a bit different that our modern view of repentance.
The word 'repent' in the Bible comes from the Hebrew word 'teshuva', literally meaning "return". The idea is, turn away from that sin and return back to God. Turning your back on your wrongs and moving to a stronger faith in God. Scriptural repentance has absolutely nothing to do with confessing one's sins to a Catholic priest.
Confession and repentance does go hand-in-hand, however. How can you repent -- turn your back on sin -- if one doesn't acknowledge and admit your sin to God? (Note that this does not require a priest or any religious person.) If you've done wrong, if you've done evil, personally admit it to God and turn your back on that sin.
First Fruits of Zion covers this in detail:
A sinner should turn back from his sin, and should confess his misdeed before God as Scripture says, “When a man or woman commits any of the sins of mankind, acting unfaithfully against the LORD, and that person is guilty, then he shall confess his sins which he has committed.” (Numbers 5:6–7) The main element is remorse in the heart, in truth, over the past; and one must take it upon himself not to do such a thing ever again. This [confession] is the essential part of repentance; but the more one confesses, the more praiseworthy he is.” (Chofetz Chaim)
It is a mitzvah of the Torah to confess our sins and repent from them. When we sin, we are not to remain in the sin, nor are we to passively accept the fact that we are sinners. We are to strive against sin. We must humble ourselves to confess the sin and then turn away from it. It is a positive commandment, to confess one’s sins and repent from them. Therefore it is a sin to leave a sin unconfessed!
Even the smallest sin should be confessed. Confession should be made privately, but audibly, directly to God. King David says, “I acknowledged my sin to You, and my iniquity I did not hide; I said, ‘I will confess my transgressions to the LORD; and You forgave the guilt of my sin. Selah. (Psalm 32:5) Yochanon the beloved disciple says, “If we confess our sins, He is faithful and righteous to forgive us our sins and to cleanse us from all unrighteousness.” (1 John 1:9)
Confession and repentance work together. It says, “then he shall confess his sins which he has committed and repent.” (Numbers 5:7) Confession is the first step toward repentance. When Yochanon called Israel to immerse as a sign of repentance, they came to be “baptized by him in the Jordan River, confessing their sins.” (Mark 1:5)
But a person may hesitate. His evil inclination will accuse him and say, “How dare I confess this sin to God? Didn’t I just confess this same sin yesterday and resolve not to do it again? How dare I come before Him again with the same offense?” When this happens, we must shove away the evil inclination from our thoughts and remember that God truly does desire our repentance. “There will be more more joy in heaven over one sinner who repents than over ninety-nine righteous persons who need no repentance.” (Luke 15:7) A person must never give up on himself. He must say to himself, “God has not given up on me, neither should I. I will try again. I will start over, brand new, beginning right now. God has surely washed me clean by Messiah’s blood. I am a new creature in Messiah. He will strengthen me to walk uprightly.”
The mitzvah of confessing our sins before God is one we can carry out confidently in Messiah. Thanks to the efficacious sacrifice of Messiah, we know that our confession and repentance will always be received. “He made you alive together with Him, having forgiven us all our transgressions.” (Colossians 2:13)