You see (or rather you won't see), the biggest change is the fact that Singleplayer as it was is no more. Instead Singleplayer will be run as a shell on top of Multiplayer, allowing for complicated things to happen behind the scenes regarding a Modders API that they are introducing in Patch 1.4. Mojang has always been a huge lover of the modding community, and now they are making tools for the modders to get access to their data in a formal manner.
What does this change mean for you, the player? Well, the game is not as sleek as it used to be, and the client will probably hog some system resources until they optimize it in Patch 1.4. Changing elements of the engine is never an easy thing (just ask Arturis), so a few of the planned bug fixes they wanted to add in with 1.3 have been pushed -- including my current pet peeve, the weird lighting bug that makes terrain turn black. But if these changes allow for great mods to start floating my way, I can be patient about the black terrain, honestly I can.
The Singleplayer/Multiplayer merge allows for some good things too, for instance now we will have the opportunity to share Singleplayer worlds across LAN. And if you're the kind of player that likes to "enhance" your gameplay in cheat mode, now the multiplayer commands like "Give" will work in Singleplayer as well.
One of my favorite new additions to the game, Villagers, are getting their trading system in 1.3, which means you can buy/sell items from Villagers. Personally this adds a huge level of immersion to the game, since now my village's inhabitants have more to do than attract zombies and randomly open and close doors.
The rumored Bonus Chest option is now officially added to the game, meaning you can start a world with a preselected set of items instead of having to scramble to create tools and build shelter in that first hectic day/night cycle. Personally I don't see myself using this option much, but it's great to have if you're building a mod, and want your players to start off with certain items tailor made for your adventure.
Other additions to Patch 1.3 include Emeralds and Emerald Ore, new terrain features (not really explained), and Tripwires so you can start laying traps for enemies (and friends if you're that sort of person.)
For the entire list of changes (and it's a big one) check out the Change Log summary. We have less than one month to wait until Patch 1.3, and the prerelease clients will be out in a couple weeks in case you're antsy.