1510s, "a composition presenting in dialogue a course of human action, the description of a story converted into the action of a play," from Late Latin drama "play, drama," from Greek drama (genitive dramatos) "action, deed; play, spectacle," from drāo "to do, make, act, perform" (especially some great deed, whether good or bad), which is of uncertain etymology.
Meaning "theatrical literature generally, drama as art" is from 1660s. Extended sense of "sequence of events or actions leading up to a climax" is by 1714. Drama queen "person who habitually responds to situations in a melodramatic way" is attested by 1992.