I am not intimately familiar with all the ins and outs of the system,
so I can't give you a comprehensive breakdown, but I can give you the
following observations:

 - 3rd edition seems much more "complete" than the previous. They've
   filled in a bunch of "holes" that existed in the past. I'm sure you
   recall that every D&D gaming circle had a laundry list of custom
   house rules to account for issues that were unaddressed in the
   book(s). Well, WotC noticed that and made fleshed out the official
   rules better to fill in those holes. (Example: they have a chart that
   shows how long it takes to don armor, both normally and "hastily".)

 - The rules have been standardized. There is now one (count 'em, one)
   chart showing experience points required per level; they don't have
   one per character class anymore.

 - The rules have been simplified. Armor class is no longer a negative
   number, but a positive number with higher values representing better
   armor. This had the effect of eliminating the table that you always
   had to consult in combat and replaced it with a simple greater-than
   test. Anytime you can eliminate a table, I say that's a win.

 - The rules are better organized. All of the various special powers for
   the various classes have been formalized as "Feats" and they have
   their own section in the book. Each character starts with 2, human
   characters get an extra feat (they start with 3), and you get a new
   feat every third level. Some classes start with "class" feats. (All
   Rangers start with "Tracking", for example.) There is a large table
   that lists the feats, including prerequisites. Example: the "Power
   Blow" Feat requires a ST of 13, the "Cleave" Feat, requires "Power
   Blow", and the "Great Cleave" Feat requires "Cleave". It's nice.

 - Most importantly, they've preserved that old-time rock-n-roll feeling
   that the original D&D had. Combat still goes lightening fast
   (something I always appreciated, especially after playing Shadowrun),
   characters still advance via levels, the classic alignments are still
   there, and charmingly-named skills like "Use Rope" are still around.

That's about it for now. Suffice to say that I like it.

Strangely, the one thing I miss is the crappy artwork in the 1st and 2nd
editions. The third edition has this stunning, full-color, glossy
WotC-ish stuff that looks like it all came from Magic cards. Oh well,
you can't have everything, I guess.