Related ideas: sin, sorry, guilt, remorse, regret, conversion, turning.
Definitions: repentance is a change of heart and mind [regarding sin]. The intent to rebel is replaced by the intent to be righteous and to act accordingly.
Greek References: μετανοια (metanoia) 3341 (Strong) cf 3326 meta, 3539 noeo 3563 nous The verb is metanoeo.
Scripture:
Repentance is essential
Luke 13:3,5 "Unless you repent you will all likewise perish"
Acts 2:38 "Repent and be baptized every one of you..."
Acts 3:19 "Repent and be converted that your sins may be blotted out..."
God moves us to repent
Acts 17:30 "God commands all men everywhere to repent"
Romans 2:4 "...the kindness of God leads you to repentance"
2Peter 3:9 "The Lord... is not willing for any to perish but for all to come to repentance"
Repentance bears fruit
Luke 3:8 "...bring forth fruits worthy of repentance"
Acts 26:18,20 "...repent and turn to God performing deeds appropriate to repentance"
Luke 15:7,10 "...joy in heaven over one sinner who repents"
Comment: Repentance is more than simply regret or sorrow for wrongs committed in the past. Repentance is a determination to change, and commitment to living righteously in the future. Repentance turns belief into obedience.