A communique is an official message that's sent between people or to a media outlet. A company might release a communique to the local newspaper announcing the name of the new CEO.
Any kind of formal announcement, report, or statement can be called a communique, especially if someone in authority issues it. Your boss might send out a communique to all her employees letting them know about a new company policy, for example. The word comes from the French communiqué, or "communicated," and even in English is often spelled with the French accent on the e — a good reminder of how it's pronounced, with a final ay sound.