the everyday third person pronoun: him, her, it, them, and in the possessive his, her, its, their
This is what the word is doing four times out of five. A Greek verb already carries its own subject inside it, so a separate pronoun is needed mainly when the person is on the receiving end of the action or is the one something belongs to. That is where this word lives: "they brought him," "his disciples," "with them." Nothing is being pressed; it is simply the smoothest way to keep referring to someone already named.
Because it is so ordinary it is the third most common word in the New Testament, behind only "the" and "and." Mark leans on it hardest, in the fast, chained storytelling that keeps a run of "he ... him ... his" moving without repeating names.
One wrinkle sits underneath the English. Older Greek had a separate word for "his own" (ἑαυτοῦ), and in the everyday Greek of the New Testament period this word was steadily taking that job over as well. In two places our printed texts mark it as the contracted form that means "his own," which is why some English Bibles read "his own" there rather than "his." The mark that makes the difference was not written in the earliest manuscripts, so it is a modern editor's call.