I'll list the differences in no particular order:
107 new Pokemon
All new region
Touch Screen Control
A new touch screen controlled Poketch that gains added functionality as you progress through the game.
Characteristics in addition to natures (Such as "Loves to Eat" or "Mischievous")
Split Attack and Sp. Atk. Attacks like Hyper Beam whose power was determined by the Pokemon's attack stat will now be determined by its sp. atk instead (since it's a beam and all?). Same goes for moves like Spark (used to be sp. atk, now attack).
New evil organization (Team Galactic)
Poffins replace Pokeblocks for boosting a Pokemon's contest condition.
New Super Contests which replace the old contests with touch controlled dress-up, dancing, and a 4-round appeal.
The Underground which allows you to dig up fossils, shards, and items called spheres which you can trade for decorations. This is also where your secret base is. You can connect to other people with this mode and do activities like capture the flag and trading decorations.
Wi-fi Connectivity which allows you to trade and battle online. Voice chat can be enabled as well.
A Global Trading Station or GTS which allows you to offer a Pokemon for a trade and ask for a certain Pokemon if you've seen it already.
Pokemon are animated when they come out of their Pokeballs like in Emerald.
The bag can now hold all items and the "Player" PC option now only deals with Mail and Ball Capsules.
Ball Capsules which allow you to decorate your Pokeballs and customize the way your Pokemon are sent out.
Pre-written messages for use in the Union Room, Mail, or Catchphrases.
A new Coin Case that allows you to carry 20000 coins. Note that the prizes will be much more expensive as well.
VS. Seeker returns from FR/LG.
Partners that team up with you allowing you to participate in Wild Double Battles.
A Pal Park that allows you to migrate Pokemon PERMANENTLY from your Gen III games after obtaining the National Dex.
A snowy area affected by hail.
Buildings and objects rendered in 3-D on the Overworld.
New Berries that allow you to reduce damage when held.
Day/Night has returned from Gen II.
Gender differences between some Pokemon. (Such as a female Pikachu having a heart-ish shaped tail.)
New moves, abilities, and items.
...And other features I'm likely forgetting.