to ignore what someone says; to ignore a cry for help. How can you just turn a deaf ear to their cries for food and shelter? Jack turned a deaf ear to our pleading.
Refuse to listen, as in You can plead all day but he's turning a deaf ear to everyone. This expression dates from the first half of the 1400s and was in most proverb collections from 1546 on. Also see fall on deaf ears.