v.1. To make something smooth and shiny by rubbing or chemical action: The jeweler polished up the stones and made them into a necklace. She cleaned the mud off her shoes and polished them up.
2. To improve one's knowledge of something, especially through study and practice: I've been polishing up on my Spanish because I'm going to Mexico. My dancing skills weren't that good, so I took a class to polish them up.
3. To improve or refine something: The mayor tried to polish up his image after the scandal. The manuscript is good, but you need to polish it up if you want it to be published.