to turn your whole life back toward God: a deep change of heart, mind, and direction, not just a feeling of regret
This word names the turning that the New Testament puts at the front of the good news. John the Baptist, then Jesus, then the apostles all open with it: the reign of God is breaking in, so turn around and live toward him. It is not first an emotion and not merely a private opinion you revise. It is a reorientation of the whole person, the kind of about-face the Hebrew prophets meant when they called Israel to come back to the Lord.
The one core idea shows up in two settings that are worth keeping apart, because the call lands differently in each. Sometimes it is the opening invitation to people who do not yet belong: turn to God and trust the good news. Sometimes it is a corrective word to people who already belong but have drifted: turn back from this particular wrong. The risen Jesus speaks this second way to his own churches in Revelation, and Peter speaks it to Simon. Same turning, different starting point.
Luke gives the word its warmest coloring. There turning is something heaven celebrates, a homecoming met with joy rather than a crawl toward punishment, and it is finally a gift God grants rather than a feat people achieve. Across the New Testament the turning is meant to show in real life: it bears fruit, it changes what a person does, and where it is refused even disaster cannot force it.