From the game guide http://us.battle.net/d3/en/game/guide/gameplay/game-difficulty
New affixes appear on monsters: Arcane Enchanted, Extra Health, Fast, Horde, Fire Chains, and Vampiric.
Champion and rare monsters can have up to 2 affixes.
Pages of Training, which are required to train artisans and craft several potent recipes, now drop.
The effectiveness of the Life Steal affix – which restores your Life by a percentage of the damage you deal – is reduced in advanced difficulties, as shown:
Also CCs like stuns and snares will be slightly less effective (stun timed shortened, movement/att speed reductions not as effective).
Also incoming damage to you will hit a lot more. If you have survived Act 4 of a previous difficulty, the beginning of Act 1 should be fairly easy, until you find your first elite. In hardcore players deal with this by making use of lots of vit, defensive skills and passives, especially ones that allow you to break CCs or run away quickly.