Check out the opening. One thing Blizzard does right, at least, is their cinematics.
New hero: The Crusader, melee character with shield and swords / hammers / flails (i.e. Paladin).
One new Act: Supposedly much more of a "dark feel."
New level cap (70): New skills and runes.
Loot runs: Entirely randomized dungeons that take 15-20 minutes to complete (for endgame).
Nephalem Trials: Currently unknown.
Expanded paragon system: Paragon levels are now account wide (applies to all characters), no more cap.
Loot 2.0: Modified loot-system, multi-level legendaries and a new system called "smart drops," loot will drop less but the drops will be better and more meaningful for you.
Transmogrification: Change the look of your stuff but keep the stats (see WoW).
The Mystic: Artisan that allows you to re-attribute the stats of your items (think reforging).
Check out all the info, news, and trailers from Gamescom 2013