Here are two answers and I hope both are clear. There are two different yet similar meanings of the word.
One meaning is that in Hebrew “hallelujah” is a composite of two words – “hallel” (praise) and “Yah” (God). Together it means “praise God”. Judaism teaches that any prayer that is completely sincere and heartfelt is the highest form of praise for God regardless of which words or phrases are said.
A second explanation is that the word “hallelujah” mentioned in Psalms is the Hebrew word for requesting a congregation to join in praise. However, according to this explanation the end of the word “yah” does not mean God (although the intent of the praise is to the Creator). "Hallel" means to recite praise, "hallelu" is the plural form. The grammatical extension "yah" is a way of expressing magnanimity. For example "merchav" means space, "merchavyah" means a vast space (Psalms 118:5); "shalhevet" means flame, "shalhevetyah" means a colossal flame (Song of Songs 8:10). Hence, halleluyah means "a great praise."
It is not a contradiction for there to be more than one interpretation for this word, as the Hebrew language does include the possibility for many meanings in the same word. Thus it can mean “praise God” and can also be understood to mean "a great praise."
