Foster mother is the non-biological mother that looks after a person after the death of their parents or their absence because of something beyond their reach or because of merely their indifference and negligence towards the kid.
For example, Curly Dadan from the notorious Mountain Bandits was by force the foster mother of Luffy and Ace after she was blackmailed by their grandfather, Garp. He disposed of them at her place and went away.
For reference, the example is taken from the anime, One Piece.
Check the following illustration of the foster mother.
Disclaimer: this illustration is not authentic and it’s solely used for the sake of demonstration.