repentance: a person's whole-life turning back to God, away from sin, that shows up in changed conduct.
The English word that fits best is repentance, but the Greek means more than feeling sorry. By the time of the New Testament this word had come to name a full turning of the whole person toward God: mind, will, feelings, and the actual direction of one's life. It is the New Testament's way of saying what the Hebrew prophets meant when they called Israel to turn back to the Lord.
You will often hear that the word literally means change of mind, since it is built from Greek pieces meaning after and mind. That is true about its origins, but it badly undersells what the word had come to mean. By the first century it no longer pointed at a mere mental adjustment. It pointed at a reorientation of a life, the kind of about-face the prophets demanded and that John, Jesus, and the apostles preached.
The single steady core, then, is a turning: away from sin and toward God, meant to remake how a person lives. The shades below are not different meanings but different settings of that one turning. John the Baptist ritualizes it in his baptism; Jesus and the apostles preach it as the response to God's good news; Luke insists it must bear fruit in deeds; Paul ties it to a grief that leads to it; Hebrews makes it the foundational turn that begins the Christian life. The word stays the same; the New Testament writers each press a different face of it.
For that reason a real repentance is never only a private regret. The text keeps tying it to its fruit, deeds worthy of repentance, and to its direction, a turning toward God. The sorrow may be real, but the heart of the word is the change of course that follows.