An epideictic speech is one designed to show off the speaker's skill as an orator.
Although epideictic is the usual form of the word (you can say it either eppyDAYKtikk or eppyDAIKtikk), personally I prefer the rarer form epidictic, because it sounds sillier (eppyDIKKtikk).
Epideictic oratory will consist of a speech praising or blaming someone. It's usually not controversial, so generally you're just telling your audience stuff they already know and agree with. It's the sort of thing you'll hear at an awards ceremony, if you can stay awake long enough.
The intrinsic boredom of such proceedings is one of the reasons, I should imagine, that encouraging a speaker to show his skill at enthralling the audience has come to be seen as such a good idea.
Word To Consider Today: epideictic. The Greek word deixis is to do with display or show. The word epideictic has hardly changed since Ancient Greek times, when it was epideiktikos.