May contain spoilers. I'll try not to state anything not already shown in trailers.
Borderlands 2 plays very differently from the original. While it keeps the base elements of RPG progression and large intertwining storyline of the original there are alot of changes to the gameplay.
Elemental damage is generally pointless on an enemy type unless it is specifically designed for it (e.g. Shock damage weapons are only useful on shielded enemies, whereas on the original shock damage would still rack up more damage than a non elemental weapon), a new elemental type has been introduced: “Slag”, when a enemy is slagged it allows you to deal double the original amount of damage you would normally deal.
The AI in the game have been improved alot (in the original, if you hit a skag in a vehicle it would either splat or stay on your bumper doing damage, but in borderlands 2 if you hit an animal with a vehicle, you bowl it over). There are a bunch of new enemies including: threshers, goliaths and stalkers.
Weapon manufacturers now have different specialities (e.g. Jakobs from borderlands 1 used to specialise in powerful weaponry but fired very slowly, in borderlands 2 jakobs weapons fire as fast as you can pull the trigger, but aren't much more powerful anymore.) S&S munitions no longer exist. Eridian weapons have been replaced with E-Tec weapons that can be found by every manufacturer and tend to fire either spikes, railgun shots, or plasma balls.
The skill tree from the first game is very similar but instead of one tree with three sides it now shows three different sides. Instead of elemental artifacts that you would equip in the first game you now have “relics” which equip to your player for added bonuses.
Borderlands 2 now supports splitscreen over the net and LAN as well allowing you to play online with a friend.
Borderlands 2 keeps the humor of the original and does a very good job of making you hate the main enemy handsome jack, by the time you fight him. It could use a few patches as items tend to fall through the map from time to time which can become frustrating especially when it is a mission based retrieveal item.
Borderlands 2 doesn't feel like borderlands, but it is still a great game, and deftinitely one not to be missed.