The "subject" of the gerund
The doer of the action expressed by the gerund can be:
the subject of the sentence: I like getting up early in summer.
He apologised for not writing for so long.
I am looking forward to hearing from you.
My mom insisted on tidying my room.
Would you mind opening the window?
the noun/pronoun or possessive preceding the gerund: Irina doesn't like people telling her what to do.
Sally's constant arguing is getting on my nerves.
I objected to him/his calling me a liar.
My mom insisted on me/my tidying my room.
Would you mind me/my opening the window?
(The possessive is more formal, and it is less common in everyday conversation.)
an indefinite or generalised subject (you, one, we, people etc.): In those days, being a student meant spending long hours in the library.
unexpressed and understood only from the context: Going home seemed to be the best idea.
Related topics:
The "subject" of the infinitive
The "subject" of the participle