"Busting your ass" is an idiom that means "working really hard".
I busted my ass waiting tables and working construction to pay my way through college.
I know that all of you have really busted your asses on this project, and I really appreciate it.
This is a colloquial expression that you use when talking to people you're comfortable with. The word "ass" is a mild swear word. You probably shouldn't use it in formal situations.
There's also another meaning of "busting your ass", by the way. It means to injure your butt by falling:
You remember that time when you slipped on the ice in the front driveway and busted your ass?