To laugh so hard one rolls about; to be convulsed with laughter; to laugh one's head off.
そのコントが面白くて、観客は笑い転げた。
The skit was so funny that the audience rolled with laughter.
子どもたちは犬の真似をして笑い転げていた。
The children imitated a dog and were rolling around laughing.
彼の失敗話に私は一人で笑い転げてしまった。
I ended up laughing my head off alone at his story of failure.