noun
maternal grandfather
Formal or written term for one's mother's father. In everyday speech, 母方の祖父 or simply おじいさん are more common.
外祖父は戦争の体験をよく話してくれた。
My maternal grandfather often told me about his experiences during the war.
母方の祖父 is the common, everyday way to say 'maternal grandfather', whereas 外祖父 is more formal and literary.
Compound of 外 (gai, 'outside, external') and 祖父 (sofu, 'grandfather'), literally 'external grandfather', reflecting the traditional patrilineal family system where the maternal line was considered the 'outside' family.