Punishment is part of justice. Seeing that somebody who does wrong intentionally and with malice suffers, proportionally, is part of the lesson that the justice system teaches.

In my opinion, punishment is important for the victim (to see that they are protected, and to satiate any craving for extra judicial revenge), society at large (to demonstrate that there is a governing body that will not let people get away with causing harm), and for the criminal themselves (to show that harmful acts will result in reprisal).

It crucially can't be the whole lesson, though. There has to be guidance, forgiveness (on a legal level), and a corrective path available to people who hurt others. Punishment on its own often just perpetuates systems that produce criminality, and isn't enough to effectively reform people who have done wrong.