The Hebrew word hallel-u-yah means “All praise God!” Hallel is praise. The u adds “all of us” making it a plural verb, hallelu, let us all praise. Yah, spelled yod-hay, is an abbreviation for YHWH (Yod-Hay-Vav-Hay), the name of God. In Hebrew Scripture it is two words, hallelu yah. Following the Septuagint’s and St. John’s Greek Allelouia, St. Jerome’s Latin Vulgate gives it consistently as Alleluia. That has become the traditional Catholic usage.
In Hebrew Scripture we find hallelu yah at: Ps 104:1; 145:1; 148:14, 149:9, and 150:5. In the Deuterocanonicals, at Tob 13:22, and in the New Testament in Greek transliteration, at Rev 19:1, 3, 4, and 6.