"Богу" is Dative case of "Бог" - "God".
Examples - Благодаря Богу (кому?) мы встретились. - Thanks to God we have met.
Молиться Богу - to pray to God.
The word is masculine and is declined so:
Nominative - Бог
Genitive - Бога
Dative - Богу
Accusative - Бога
Instrumental - Богом
Prepositional - Боге