What does "bust a gut" mean?

Exert one-self to the utmost. For example, He was busting a gut trying to please her. This hyperbolic term alludes to hurting one's mid-section through physical straining. The first slangy term dates from the early 1900s, the variant from about 1700. For a synonym, see break one's ass.

Explode with strong feeling, especially laughter or anger. For example, Gene almost bust a gut laughing, or The foreman will burst a gut when he learns that the machine isn't repaired. The former dates from the late 1800s, the latter from about 1940.