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In the beginning of The Legend of Zelda: The Wind Waker she gives Link the Hero's Clothes for his birthday. She also gives Link the Hero Shield, seeing how Link's sister, Anju, has been kidnapped. Later in the game when Link returns he finds that his grandmother is sick. She is fearful that she'll lose both of her grandchildren. Link heals her with a fairy in the bottle.
A theory about Link's Grandmother is that she had a love interest with Lenzo, the photographer at Windfall Island, since Lenzo mentions he had a previous relationship with a women at Outset Island. Link's Grandmother seems to be around the right age for him. Which could mean that Lenzo is Link's Grandfather.