Hallelujah is both an exclamation –- Hallelujah! –- and what that act of exclaiming is called. When hallelujahs ring through the church, a lot of people are yelling "hallelujah!" Kind of like "bingo!" in the church basement.
Hallelujah came into English through Latin and Greek, but originally comes from Hebrew, where it means "praise the lord." In spite of traveling through those languages, hallelujah's meaning has not changed. Remember that the "j" in hallelujah is pronounced like a "y."