1encourage the development of (something, especially something desirable):the teacher’s task is to foster learning
develop (a feeling or idea) in oneself:appropriate praise helps a child foster a sense of self-worth
2bring up (a child that is not one’s own by birth):a person who would foster Holly was found
British (of a parent or authority) assign (a child) to be brought up by someone other than its parents:when fostering out a child, placement workers will be looking for a home similar to their own