Rejoicing is celebration or festivity. There will be great rejoicing when your favorite cousin comes home after his three years away in the Peace Corps.
You can use the word rejoicing as a noun, to mean jubilation and joy, or as an adjective to mean "joyful." A rejoicing crowd is full of happiness and cheer, and a rejoicing child might jump up and down with excitement. Rejoicing comes from the verb rejoice, which is rooted in the Old French word rejoir, a combination of the intensive re and joir, "be glad."