Honorific term used to refer to someone else's parents respectfully. Not used for one's own parents.
How are your parents doing?
I greeted her parents.
His parents are very kind people.
The student's parents are worried about his future path.
ご両親 is the everyday polite way to refer to someone else's parents, while 親御 sounds more formal and old-fashioned, often used by teachers or officials.
父母 is a formal, written term for 'father and mother' with no honorific nuance, unlike 親御 which specifically honors another person's parents.
親御 is the honorific term used only for someone else's parents, while 親 is the plain, neutral word for parent(s) usable for anyone including one's own.
親父 casually means 'my dad' (or an old man) and shares the kanji 親, but 親御 is a respectful term for someone else's parents, not one's own father.
Used because 親御 (someone's parent) refers to a person, so it's counted by number of people.
(someone else's) parents
Compound of 親 (oya, 'parent') and 御 (go, honorific prefix). The reading おやご is a sound shift from おや + ご.