Baldur's Gate II takes everything the original Infinity Engine RPG did and then does it better. Higher resolution, improved interface, more character class options. And then it adds more. And more. It's simply the pinnacle of 2nd Edition Dungeons and Dragons brought to computer game form.
Baldur's Gate II resumes shortly after the end of the original game- the player character and a few of his compatriots have been captured by a powerful wizard, and must first escape, then unravel the mysteries surrounding the wizard. Along the way, you clear trolls out of a keep, battle dragons, face beholders, mind-flayers, and other classic D&D monsters, and perhaps most notably, you meet an interesting array of memorable characters. While the first Baldur's Gate had some occasional party banter, Baldur's Gate 2 gives them much more to say. This is the game that established Bioware as writing such great characters, and they're all well-written and voiced. You'll remember what a jerk Anomen is, you'll remember Jan Jannsen's rambling stories, and be glad to charge into battle with your crazy-awesome, butt-kicking for goodness pal Minsc.
This was also Bioware's first game to feature romance options- a choice between the sweet and innocent mage Aerie, the practical and no-nonsense Jaheira, and the scheming priestess Viconia (I'm sorry, apparently female player characters only get that jerk Anomen as a choice). The dialogue in the sub-plots is well suited to each character's personality, and the characters will in fact bicker with each other if you're trying to be a player and romance more than one of them. It adds emotional depth to the story, particularly in the expansion (although it's impossible to explain just why without massive spoilers).
On top of this- there's the combat. The real-time-with-pause system is improved here, giving you more options on how to play, and the expanded character classes give you many more possible abilities to choose from. Numerous spells, weapons, armors, and items that didn't exist in the original game allow you to fight ever more powerful and challenging enemies.
The music is also great. You'll find this out as soon as you boot up the game. The graphics are a little dated today, but the fact that it uses painted 2D backdrops and animated sprites for characters means it hasn't aged as badly as 3D rendered games of the era have.
So play it. And be richer for it.