Link's Grandma is one of the first characters to be introduced in The Legend of Zelda: the Wind Waker. She lives on Outset Island -- and gives Link his shield after he has met Tetra.

Further on in Link's quest, he should return to his Grandma and check in on her. See: Outset Island: Jabun.

Link can receive the Elixir Soup from her by curing her with the help of a Fairy.