Lord of Destruction improves upon the original D2 in almost every way imaginable and brings a lot more replayability to the game.
The original Diablo 2 was all about depth of gameplay. Lord of Destruction increases the depth of gameplay and playability of the game in a lot of expected (and unexpected) ways. The most noticeable changes are the new classes, the 800x600 mode (which works great even on my lowly P2 266), the increased stash size, and the addition of more hotkeys for skills.
But Blizzard didn't stop at simple gameplay tweaks. The new Act V is my new favorite Act in the game. It has the neatest quest rewards (+10 permanent resist all is a huge quest reward!) and the most varied monsters of any act. The improved mercenaries add a whole new dimension to the game -- choosing the right mercenary for your party/character class can now make your character a lot more effective in combat, and best of all, except vs. the end of Act bosses, the Mercenaries actually survive long enough to do you some good, especially since you can equip them with items to make them even more powerful.
Finally, the addition of hundreds of new types of items, set items, unique items, and runes make gathering treasure a lot more fun. Since you actually have enough space to store complete sets in your stash, it is much easier to complete sets with one character rather than having to create "mule" characters to hold items for you. Item sets have become a lot more powerful because now there are hidden bonuses for partially completing a set that are cumulative with the bonuses for completing the entire set. This is especially fun on the larger sets like Sigon's Complete Steel, which gives you a page full of modifiers if you are patient and lucky enough to complete the set. There are also new uses for socketed items -- you can now find jewels (gems with better and multiple modifiers) and runes to put in item sockets. Find the right combination of runes, and you can create very powerful Runeword items that can be even better than some of the best set items and uniques in the game.
Finally, Blizzard tweaked a lot of little things in the game to improve game balance and reduce lag which, while taking a little time to get used to, improve the overall gameplay experience. I mention this because Blizzard is one of the few game companies that still fix problems in their games one, two, or three years after release. With some game companies, you are lucky to get patches six months after the game release.
The expansion is about $10 too expensive for what it adds to the original game. I experienced consistent crashes in network play when playing an Assassin with my friend's Druid, but to be fair, Blizzard was very responsive to my bug reports.
The Bottom Line
Diablo 2: Lord of Destruction fixes most of the gameplay problems of the original Diablo 2 while adding a lot of depth to the game as well.