This phrase can have several meanings. Most often it is used when someone goes on vacation, to a party, on a visit, and you wish him to have a good time. But отдых also means resting, so it would be quite appropriate to say “Хорошего отдыха!” before going to bed.
Pronounced like: [харо́шыва о́тдыха] / [haróshyva ótdyha].
English variant — Have a good/nice rest!
Usage example: Уже поздно. Всем пора спать. — Хорошего отдыха! Увидимся завтра. — It’s already late. It’s time for everyone to sleep. — Have a nice rest! See you tomorrow.