Hard mode changes the gameplay compared to Normal in some ways to make it more difficult.
When playing in hard mode, a small red pentagram () appears on the HUD, below the consumables.
Rooms contain more advanced enemies and in a higher number.
Causes champions to spawn more often; however, they award fewer pickups.
You are 65% less likely to receive hearts after completing a room.
Only champion bosses can drop red hearts; normal bosses will not.
Prior to update 1.03, the reduced drop-rate affected all Pickups (not just Red Hearts).
Godhead's unlock requirements were extended in the Afterbirth DLC (and further extended in the Afterbirth+ DLC) due to the addition of more completion marks, but it can still be unlocked in the base game using the same method.