means A person who writes plays for the stage.

from A compound of "play" plus "wright" — and that second half is the surprise. A wright was a maker or builder, the same word lurking in "wheelwright," "shipwright," and "cartwright." It comes from Old English "wyrhta," a worker or craftsman, related to the verb "work." So a playwright isn't a play-writer at all (despite the homophone tempting everyone to spell it "playwrite") but a play-builder — someone who hammers and joins drama together like a carpenter assembling a chair. The coinage is fairly modern as English compounds go, an early-17th-century formation, and the craftsman framing was apparently meant as a bit of a jab, suggesting a mere maker of plays rather than a true poet.