An onnagata is a "male actor playing a female role exemplifying ideal, ultimate womanhood." Although a woman, Izumo no Okuni, originated the kabuki form in 1603, male actors have played all roles since a ban was placed on female performers (1629 C.E.) and boys (1652 C.E.) by the Tokugawa Shogunate.
You can learn more about kabuki online or in numerous scholarly works. The Wikipedia article turns out to be a pretty good general overview.
Of the sources I originally used and painstakingly verified on 7/25/1997, all are now offline (thanks to Heather Johnson for pointing that out!). They were:
Last updated November 8, 2011.
©1997, 2011 Alan P. Scott. All rights reserved.