What does Luke 15:21 mean?

This is a beautiful example of whole-hearted repentance. The prodigal son found himself penniless and starving, used by acquaintances in the same way he had used his father. Finally, in desperation, he acknowledged his sin, recognized he needed to repent, and immediately set out to do so (Luke 15:13–19). "While he was still a long way off, his father saw him and felt compassion, and ran and embraced him and kissed him" (Luke 15:20). The son could have stopped there. He could have accepted his father's love and hoped his father knew his intent, leaving no reason to say anything more about it.

For the first time, however, the son has the humility and integrity to own his shame. He fully realizes his position before his father and wants to live out of that truth. With that, he has fulfilled his responsibility. This is biblical repentance: acknowledging the truth about our sin and rebellion against God, desiring to change our ways, and asking Him to forgive us. This is not a work—a deed or an action—we must do to earn forgiveness. It's merely accepting and living out reality. To call it "work" throws contempt on the true work Jesus accomplished by hanging on the cross and taking the wrath of God our sin deserved.

Despite his plan (Luke 15:19), the prodigal son doesn't offer to be his father's servant. The father's display might make this inappropriate or the son may realize that even that offer would be an attempt to earn something he doesn't deserve. He is content to accept his father's decision. With the son's repentance, the rest is up to the father.