Ezlo is a renowned Minish sage who was working on creating a cap that would grant a wish to the person that wore it, a gift for the human race from the MInish. His apprentice, Vaati, craved the power of the cap and decided to steal the cap from Ezlo when he wasn't expecting it. Taking control of the cap, Vaati used his newfound powers to transform Ezlo, rendering him harmless. Now a powerful sorcerer, Vaati heads for Hyrule Castle and turns princess Zelda to stone before releasing hordes of monsters upon the land of Hyrule.
While on his quest to rescue Zelda, Link runs into Ezlo in the Minish Forest and saves him from an Octorok assault. Ezlo explains his story and discovers that they have a common goal, defeating Vaati and thus decides to join Link on his quest, comfortably on top of his head. Ezlo is a great asset for link, providing advice (and sass) as well as ability to shrink Link down to Minish size through portals scattered around Hyrule.