Polite, somewhat old-fashioned term for one's own mother. Often used in formal or respectful contexts, but may sound stiff in casual conversation.
ははごはどちらにいらっしゃいますか。
Where is your mother?
ははごによろしくお伝えください。
Please give my regards to your mother.
Compound of 母 (はは, 'mother') and honorific suffix 御 (ご). The exact historical development is uncertain, but it follows a pattern of polite forms with 御.