This is the 2086th most frequent Russian word.
моя
"Моя" means "my" (feminine form).
In this sentence, 'моя' (my) is used as a possessive pronoun that refers to the feminine noun 'кошка' (cat).
Моя кошка всегда спит на диване.
My cat always sleeps on the sofa.
Here, 'моя' is again a possessive pronoun used before 'любимая книга' (favorite book), where 'книга' is a feminine noun.
Это моя любимая книга.
This is my favorite book.
In this sentence, 'моя' should be 'мою' to correctly form the accusative case of the feminine noun 'сумка' (bag).