"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 Psalter Hymnal (see the index of first lines).

Liturgical Use:
As an independent acclamation traditionally with the reading of the gospel, but appropriate at many other times in worship; as a frame around another psalm or hymn, for example Psalm 70 (sing either "alleluia" or "maranatha").

--Psalter Hymnal Handbook

Jacques Berthier composed TAIZÉ ALLELUIA for use at the Taizé Community (see PHH 217, 312, and 622 for further discussion of this community and its music). Known as ALLELUIA VII in Taizé publications, the tune functions as the communal refrain for stanzas that are sung by a cantor. It became better known in the English-speaking world after its publication in Music from Taizé (vol. 2, 1984).

Sing in harmony with great inner intensity. This tune works well unaccompanied, but in Taizé style various instruments would be used in repetitions of this short refrain.

--Psalter Hymnal Handbook