noun
mother-in-law; stepmother; foster mother
Refers to a mother by marriage or legal relationship, not by blood. Context determines whether it means mother-in-law, stepmother, or foster mother.
義理の母と同居しています。
I live with my mother-in-law.
彼女は私の義理の母で、父の再婚相手です。
She is my stepmother, my father's second wife.
姑 specifically means mother-in-law (husband's or wife's mother) and can carry a traditional or slightly negative nuance, unlike the neutral 義理の母.
Compound of 義理 (giri, 'duty, obligation, relationship by marriage') + の (no, possessive particle) + 母 (haha, 'mother'). Literally 'mother of obligation/relationship'.