I go through everything new in the 1.3.1 update here is a list of everything i talk about:
Single Player Runs on a Server Internally
Single Player Commands
Bonus Chest (Optional, Added through world Creation settings)
Adventure Mode (Optional, Added through world Creation settings)
Trading With Villagers Using Emeralds!
Jungle Trees Have a chance of spawning with Cocoa Beans
EnderChests have been added to the game.
TripWires have been added to the game.
There is a new creative inventory.
You gain Experience from mining and smelting.
You can now write in books.
New World Type called "Large Biomes"
Added a temple in the Desert (Also supposedly in the jungle yet i could not find one)
You can now chat (There is also chat settings In-Game by pressing "ESC")
There is apparently a new F3 info screen.
Minecraft now has a Demo for Non-Premium uses (People who have not brought the game)
/seed command Allowing you to see the seed for the world you are in.
/defaultgamemode (For multiplayer on your singleplayer world, allows you to set the default gamemode e.g. Creative/Adventure/Survival for when a new player joins your game)
The Maximum level for enchanting items is no Level 30 not Level 50.
/tp now has the ability to tp you to a certain coordinate.
Mobs now spawn on Half Slabs and Upside Down Stairs
Items AutoStack when in Entity form and near each other.
Stars are now Smaller and Brighter at night.
The sky in "The End" is changed.
Some new items are now stackable (I am unsure as to exactly what items)
The texture for Gravel has been altered.
Levers can now be placed on the roof.
Creepers' Explosions damage is now modified depending on the difficulty of the world.
You can buy this game at http://www.minecraft.net