To rejoice is to be incredibly happy, or to express your incredible happiness. If you just won millions in the lottery, you might rejoice by screaming at the top of your lungs.
When you rejoice, you celebrate or feel extreme happiness. You might rejoice after scoring the winning goal in a championship game, or you might rejoice when you receive an amazing gift on your birthday. You’ll often hear this word in the phrase “let us rejoice,” especially in some religious settings.