Peter MacCallister is Kevin's dad, but he's not really as important to the story as Kevin's mom. Sure, he loves Kevin and all that typical dad stuff, but he's not the one who goes on a quest to get back to Kevin as soon as possible.
He's content to wait for the next available flight back from Paris—which, ironically, gets him back to Chicago at the same time as Kevin's mom.
But Pete plays an important role at times. For instance, he inadvertently gives info about the house's security system (automatic timers on the lights) to fake police officer Harry, which allows Harry and Marv to try to rob the house.
Also, the whole reason the McCallister family is going to France is because Pete's brother lives in Paris. So, Kevin's dad provides the initial impetus for the entire action of the movie, in a way.
After they're on the plane, Kevin's mother feels like they forgot something. But Pete thinks he just left the garage door open, saying: "That's it. I forgot to close the garage. That's it."
This is true actually, but Kate's the one with the parental intuition, the sense to realize that they actually forgot Kevin. So Pete's a bit more of a background character—he doesn't get a lot of funny lines, or sudden realizations or moments of action. He just helps set the stage.
In the end, Kevin's dad finds Harry's gold tooth on the floor—the only remaining evidence that anything had happened, since Kevin keeps his mouth shut about what went on with the burglars. Either it will remain a permanent puzzle, or he'll learn the violent truth…