To "mess up" something means to break it or make it ruined. The word "break" is used for things that break into separate pieces, or machines that don't work any more. But "mess up" can be used for a wide variety of situations. For example:

• mess up a project
• mess up your relationship with someone
• mess up someone's car
• mess up someone's face (by hitting them and giving them bruises)
• mess up a recipe that you're cooking