"Straightening up" is a type of cleaning. When you "straighten up", you pick up things that are lying around like clothes, dishes, books, pieces of paper, and so on. You put things back in their proper place, so that the room looks organized.
You can use "straighten up" with an object:
Lance, straighten up your room please.
Or you can use it without an object:
Sorry, I didn't have time to straighten up.