Witch's House
Throughout the franchise, a Witch's House has been an area where Link can find secrets or collect potions. Sometimes, the witch will give him a special item that is important to a Side Quest. 3 Dimensional Zelda games don't have Witch Houses, excluding Ocarina of Time.
In A Link Between Worlds
The Witch's House is a location in A Link Between Worlds. It is the house of Irene and the Witch.
Location
The Witch's House is found exactly where it was in A Link to the Past: north of the Eastern Palace yet south of the Zoras.
Purpose
The Witch's House acts as the Potion Shop of A Link Between Worlds. It is here Link can buy a Red Potion, Blue Potion, Yellow Potion, or Purple Potion. While the Red Potion can be bought with rupees alone, the blue, yellow, and purple potions require ten of either Monster Tails, Monster Horns, or Monster Guts, respectively.