Old English blæst "blowing, breeze, puff of wind," from Proto-Germanic *bles- (cf. Old Norse blastr, Old High German blast "a blowing, blast," German blasen, Gothic blesan "to blow"), from PIE *bhle- "to blow," probably a variant of root *bhel- (2) "to blow, inflate, swell" (see bole).
Meaning "explosion" is from 1630s; that of "noisy party, good time" is from 1953, American English slang. Sense of "strong current of air for iron-smelting" (1690s) led to blast furnace and transferred sense in full blast "the extreme" (1839). Blast was the usual word for "a smoke of tobacco" c.1600.