An encomium is a fancy word for a formal speech or piece of writing that warmly praises someone or something.
Encomium comes from the Greek word enkomion which, in a nutshell, is to honor someone or something at a party in a poetic speech. It used to refer to the song for the winner of the Olympic Games, sung at a victory celebration. You might hear an encomium at a retirement party, after you publish a fabulous book, or even at a funeral (a eulogy, or speech at a funeral about the person who died, is a kind of encomium). It's pronounced with a long O, en-CO-mium.