This is the 8358th most frequent Russian word.
моему
"To my" or "to mine" (dative case of "мой," meaning "my").
The word "моему" is used in the dative case as it indicates to whom the book was given.
Я дал книгу моему другу.
I gave the book to my friend.
Here, "моему" is in the dative case, showing possession or connection to the noun "брату" in the direct context.
Это принадлежит моему брату.
This belongs to my brother.
"Моему" is again in the dative case, specifying the recipient of the news.