Forms of the word “repent” or “repentance” are used in the New Testament 66 times in 60 verses. The majority of the time it is translated from the Greek words μετάνοια (met-an'-oy-ah), noun, and μετανοέω (met-an-o-eh'-o), verb. It simply means “a change of mind.” Eight of the occurrences in the New Testament “repent” are translated from a form of the Greek word “μεταμέλλομαι (met-am-el'-lom-ahee)” and it can have a meaning of “caring afterwards, or “regret.” In contrast to the OT words for repentance, these two words are always translated as some form of the word “repent.”
Neither the object of the change of mind nor the result of the change of mind are in the meaning of the word. Those must be determined by the context.
We are not told in the Bible to repent in order to be eternally saved. We are told to believe in Jesus.
Most of the NT meaning of repentance is summarized by Jesus’ assessment of the Ninevites who repented after Jonah’s teaching; they turned from their evil way and escaped some sort of temporal judgment. (Matt. 12:41; cf. Jonah 3:12).
Application to those who are saved by grace through faith: When we sin we are exhorted to confess our sins for forgiveness, cleansing, and restoration to fellowship (1 John 1:9) When this is neglected we need repentance.