This is the 1952nd most frequent Russian word.
своём
"Своём" means "one's own" (in the prepositional case).
In this sentence, 'своём' is a possessive pronoun referring to something belonging to the subject (он). It agrees in gender (neuter), number (singular), and case (prepositional) with the noun 'доме'.
Он думает о своём доме.
He thinks about his own house.
Here, 'своём' indicates possession and corresponds to 'her own'. It modifies 'решении', showing prepositional case agreement with it.
Она рассказала о своём решении.
She talked about her decision.
The word 'своём' in this sentence acts as a possessive pronoun indicating ownership ('our own'), matching the gender (masculine), number (singular), and case (prepositional) of 'выборе'.