"Alleluia" is the Greek spelling of a Hebrew expression, "Hallelu Yah[weh]," which simply means "praise the Lord." That phrase is found in the Old Testament as a frame around a number of the psalms (Ps. 103-106; 146-150) and in the New Testament in Revelation 19: 1-6. In Christian liturgical use "alleluia" is usually sung in conjunction with one of the Scripture readings as an acclamation (except during Lent). It is also used during Easter and appears as a phrase in many hymns. Some musical settings of "alleluia" are overtly jubilant; for example, George F. Handel's famous "Hallelujah" chorus in The Messiah. But there are many ways to sing "alleluia"-note all the "alleluia" hymns in the Psalter Hymnal (see the index of first lines).
Psalter Hymnal Handbook