This is the 3154th most frequent Russian word.
матерью
"Матерью" means "by (or as) mother" in English, as the instrumental case of "мать" (mother).
In this sentence, 'матерью' means 'mother' in the instrumental case, following 'была' to indicate the role or quality of being a mother.
Она была прекрасной матерью.
She was a wonderful mother.
Here, 'матерью' is in the instrumental case, showing the focus of the child's pride.
Ребёнок гордится своей матерью.
The child is proud of his mother.
Although 'матери' is used here, the switch to 'матерью' in related contexts highlights the instrumental role it plays, emphasizing the caring relationship.