According to Webster's 1913, epideictic means "Serving to show forth, explain, or exhibit;--applied by the Greeks to a kind of oratory, which, by full amplification, seeks to persuade."
(There are a bunch more rhetorical terms at Everything2, among other places.)
But MW3 says it means "designed primarily for rhetorical effect." Which seems like a kind of meta-rhetorical term--aren't most rhetorical figures designed primarily for rhetorical effect?
MW3 helpfully provides a synonym: "demonstrative." I've never heard that term applied to rhetoric before, so I looked it up--and meaning 3 of demonstrative is (I quote in full): "epideictic."
I'm always pleased when I encounter a definition loop in a major dictionary.
Fortunately for my poor brain, the BYU website has a section on oratory (Silva Rhetoricae), which includes a page for epideictic oratory, which more or less explains how the above definitions fit together:
The Greek epideictic means "fit for display." Thus, this branch of oratory is sometimes called "ceremonial" or "demonstrative" oratory. Epideictic oratory was oriented to public occasions calling for speech or writing in the here and now. Funeral orations are a typical example of epideictic oratory. The ends of epideictic included praise or blame, and thus the long history of encomia and invectives, in their various manifestations, can be understood in the tradition of epideictic oratory.
So I guess it was more about public speeches of praise or blame than seeking to persuade. I'm not quite sure how to reconcile that with the Webster's 1913 definition.
Some day I should sit down and read a good book on rhetorical devices. I can never remember which names go with which figures, or even what half the figures are.