What does Luke 13:3 mean?
Jesus has just finished telling His audience that if they have wronged another person, they need to reconcile before the dispute reaches the court. It's far better to admit you're wrong and pay what you owe than it is to risk the magistrate declaring you guilty and sending you to prison (Luke 12:57–59). Now, people from a crowd listening to Jesus spread news: Pilate has slaughtered some Galileans who had gone to Jerusalem to offer sacrifices. Jesus gives a hard truth: they did not deserve this violence and it could happen to anyone (Luke 13:1–2).Jesus compares the fate of the Galileans to the eternal fate of anyone who wrongs God and does not repent. The Galileans died physically because they were not reconciled to Pilate; in a similar way, anyone who dies without being reconciled to God will die spiritually. They will spend eternity in hell—a far greater punishment than prison and fines.
The concept of "repentance" is sometimes difficult to grasp. Literally, it means "to change one's mind." It means to acknowledge you did something wrong, agree you need to not do it again, and endeavor to stop doing it. There are two different spheres of repentance. The most important is repentance that leads to salvation. We need to admit that we are sinners, admit we have wronged God, ask for His forgiveness, and agree that we need to change our actions. The second is relational repentance. We admit that a specific action is wrong and we need to quit doing it; this is not necessary for salvation, but it restores our fellowship with God. Sometimes we need to repent many times for the same sin.
Some scholars think Jesus' address is directed the Jews as a nation and "perish" refers to the violent destruction of Judea in AD 70. There's no solid indication this is so. Jesus is telling the individuals in the crowd that they need to repent. The next section, Luke 13:6–9, more specifically refers to the nation of Israel.