Diablo 3 Difficulty Levels

Diablo III is not over when you finish its final Act. After completing Diablo III on Normal difficulty, you’ll unlock a new difficulty level with which you can continue the game:Nightmare.
If you survive the increased difficulty and complete the game on Nightmare, you’ll unlock the even more challengingHell level. And, if you’re able to best Hell…Inferno awaits.
You will carry your existing character (and all of that character’s levels, skills, powers, and equipment) over to the new difficulty level – but that doesn’t mean you’ll be free to squash helpless demons. Using your existing character on a new difficulty level is necessary. You’ll need every advantage you can get just to stay alive.
In Nightmare and Hell mode (and beyond), you’ll continue to gain levels and skill runes, but you will also find items, gems, potions, armor, and weapons only available in these difficulty levels. As you grow in power, so too will your enemies.
Once you've reached level 60, defeating certain bosses grants you a temporary boost to your abilities called Nephalem Valor. This lasts 30 minutes, persists through death, and stacks with other Nephalem Valor buffs up to five times. Each Nephalem Valor buff provides a 15% increase to the Magic and Gold Find statistics.
Good hunting.

Hardcore Characters

You can create a hardcore character from the character creation page after reaching level 10 with any Diablo III hero. Hardcore characters begin playing Diablo III at Normal difficulty and advance through subsequent difficulties just like normal characters. They differ from normal characters in one crucial area, though:
IF YOUR HARDCORE CHARACTER DIES, THAT CHARACTER IS PERMANENTLY DEAD. They will never be playable again. There is only one way to successfully play a hardcore character: don’t die.
Hardcore characters have access to the hardcore-specific gold auction house, but are unable to purchase items from or sell items to non-hardcore characters. They cannot use the real money auction house. Hardcore characters can only share the items in their stash with other hardcore characters on your account.
Hardcore characters are not recommended for the faint of heart.