In a large part, a distraction. Or more generally, a way to stay in power. How do you stay in power when your country is doing very poorly economically while you and your friends keep siphoning public money into their pockets? You create a strong narrative, ideally an external enemy ("NATO wants to destroy our way of life!" "Ukraine is full of fascists killing Russians!"). Support it by propaganda from your state-controlled media and you are a hero saving the country, if not the world. You can do pretty much anything and still retain considerable support.

That's also why Putin can't really afford peace, he would lose a strong narrative in his favour. He pretends to agree, but doesn't actually follow conditions of any agreement while constantly increasing his demands. He might agree with an agreement that would basically be Ukraine's capitulation, but nothing less.