The Horadric Cube is a portable Ender Chest.
If the player is going through the main quest line, the Horadric Cube will first be encountered in the Chapter 1 quest "The Horadric Cube," when it is crafted by the Avalon citizen Velore. He crafts this item out of an emerald, redstone dust, a gold ingot, and a stone brick block. Of the first three ingredients, Velore says the following:
"Emeralds are naturally imbued with magical essence.
The Redstone Dust allows us to properly channel the Emeralds' magical essence...
A Gold Ingot will infuse your Cube with trans-dimensional Properties."
If you lose your cube, you can buy another one from the Magic Shop located in your Guardians' Tome.