Refers to the mother of one's spouse. The most common meaning of 義母.
義母は料理がとても上手です。
My mother-in-law is very good at cooking.
A woman who raises a child not biologically her own, in a formal or legal fostering arrangement. Less common than the mother-in-law sense.
彼女は幼い頃から義母に育てられた。
She was raised by her foster mother from a young age.
The wife of one's father who is not one's biological mother. Can be used in both legal and informal contexts.
義母とは最初はぎこちなかったが、今は仲がいい。
At first things were awkward with my stepmother, but now we get along well.
I've been living with my mother-in-law since I got married.
My wife is always careful to be considerate toward her mother-in-law.
My husband's sister and I take turns caring for our mother-in-law.