At the close of the performance of a comedy in the Roman theatre one of the actors dismissed the audience, with a request for their approbation, the expression being usually plaudite, vos plaudite, or vos valete et plaudite. [William Smith, "A First Latin Reading Book," 1890]
English used it to mean "drive out with violence and sudden noise" (1650s), later, "go off with a loud noise" (American English, 1790); sense of "to burst with destructive force" is first recorded 1882; of population, 1959. Related: Exploded; exploding.