This would mean that something was very funny. The image is of you laughing so hard your sides burst open. It's an exaggeration.
Well, darling, a sidebuster is slang for a person who is an outsider or an uninvited guest at a social gathering. So, if you find yourself crashing a party or sticking your nose where it doesn't belong, you might just be labeled as a sidebuster. Just remember, it's always better to be the life of the party than the one everyone wishes would just bust on out of there.
Oh, dude, so like, back in the wild west days, cowboys would call people "sidebusters" because they were basically like, newbies or greenhorns who didn't know much about ranching or cowboy life. It was kind of like teasing them for not being as experienced or skilled as the seasoned cowboys. So, yeah, it was just a playful way of poking fun at the rookies.