"Hard mode" is the difficulty you set as you create a character, according to the 1.0.6 patch notes:
There are now 3 difficulty modes that are set when creating a character.
○ Softcore - Drop coins on death, keep max hp and mana values.
○ Mediumcore - Drop all items on death, keep max hp and mana values.
○ Hardcore - Drops all Items and deletes your character on death, requiring you to start a new character. On death you will become a ghost that can not interact with the world until you log out.
