From Diablo Wiki
The Horadric Cube is a powerful artefact made by the Horadrim brotherhood, capable of magically merging or transforming objects inside it. The box outer size is significantly smaller than the inside.
The Horadric cube features prominently in Diablo II, and you can read more about the .
 The Cube in Diablo III
There is no direct analogue for the Horadric Cube in Diablo III. D3 has a Nephalem Cube which is sort of similar in function, where the player may choose to place items inside of it, and then break them down for crafting materials. However, unlike the Horadric Cube, the Nephalem Cube is not stored in the inventory, and the Nephalem Cube cannot be used to store items. It is embedded into the inventory pane of the UI, and can only be used to break down items. It doesn't offer extra storage, nor is it used as a crafting catalyst to create items. That function is now carried out by the Artisans.