Within the Hebrew Bible, halelu yah functions as a structural marker rather than free composition: it opens and closes specific psalms in the two blocks that use it, 113 through 118, known collectively as the Hallel and recited at Passover and other festivals, and 146 through 150, the closing sequence of the entire Psalter, so its appearances are concentrated and formulaic rather than scattered evenly through the biblical poetry. Its single New Testament occurrence, in Revelation 19, places it in a heavenly liturgical scene of praise, and it is this Greek transliteration in Revelation, alleluia rather than a translated phrase, that fixed the word's exact form for the Christian liturgical tradition that followed, rather than any direct continuous borrowing from synagogue practice.
One of the more distinctive things later Christian liturgy did with the word, unrelated to anything in its biblical use, is suppress it seasonally: the Western church developed a practice, well established by the early medieval period, of omitting Alleluia entirely during Lent, so that its return at the Easter vigil functions as a marked liturgical event, the reintroduction of a word deliberately withheld for weeks precisely so its reappearance can be felt rather than simply heard. Eastern liturgical practice treats the word differently again, retaining it through Lent in a more subdued musical setting rather than removing it outright, so the two halves of Christianity that inherited the same Hebrew word built two different seasonal disciplines of withholding and restoring it, neither of which has anything to do with the term's original festival use in the Hallel psalms.