This is the 2704th most frequent Russian word.
богу
"Богу" means "to God" in English (dative case of "Бог").
In this sentence, 'богу' is used in the dative case, indicating the recipient of the action of the prayer.
Я молюсь богу о помощи.
I pray to God for help.
Here, 'богу' is again in the dative case, indicating he is the one to whom lives are entrusted.
Мы доверяем богу наши жизни.
We entrust our lives to God.
In this sentence, 'богу' is in the dative case, used in a passive grammatical construction to denote the entity receiving responsibility.