1530s (transitive), "to reject with scorn," from Latin explodere "drive out or off by clapping, hiss off, hoot off," originally theatrical, "to drive an actor off the stage by making noise," hence "drive out, reject, destroy the repute of" (a sense surviving in an exploded theory), from ex "out" (see ex-) + plaudere "to clap the hands, applaud," which is of uncertain origin. Athenian audiences were highly demonstrative. clapping and shouting approval, stamping, hissing, and hooting for disapproval. The Romans seem to have done likewise.
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 "cause to burst suddenly and noisily" (1794). Intransitive sense of "go off with a loud noise" is from 1790, American English; figurative sense of "to burst with destructive force" is by 1882; that of "burst into sudden activity" is from 1817; of population by 1959. Related: Exploded; exploding.
"expression or round of applause, praise bestowed with audible demonstrations," 1620s, short for plaudite "an actor's request for applause" (1560s), from Latin plaudite! "applaud!" second person plural present imperative of plaudere "to clap, strike, beat; applaud, clap the hands; approve," a word of unknown origin (also in applaud, explode). This was the customary appeal for applause that Roman actors made at the end of a play. In English, the -e went silent then was dropped. Related: Plauditor; plauditory.
1729, intransitive, "explode suddenly and loudly," a back-formation from detonation, or else from Latin detonatus, past participle of detonare. Transitive sense of "cause to explode" is by 1801. Related: Detonated; detonating.
As a noun, it is recorded from 1809 in the sense "outburst, quarrel;" 1807 as "an explosion." Meaning "enlargement from a photograph" is attested by 1945 (the verbal phrase in this sense is by 1930). Old English had an adjective upablawan "upblown," used of a volcano, etc.
1825, "person in ragged clothing," from duds (q.v.). Sense extended by 1897 to "counterfeit thing," and 1908 to "useless, inefficient person or thing." This led naturally in World War I to "shell which fails to explode," and thence to "expensive failure."