Dragon Ball Kai is a rebroadcasting of Dragon Ball Z. Basically, they're reducing the show from 300 to 100(ish) episodes. They're cutting out 'fillers' and less important scenes to follow the manga closer. They've also re-recorded all the voices and touched up the animation.
I loved this show so much when I was in grade school. Oddly enough, I still do! At the end of each episode I find myself excited for the next episode. I know everyone made fun of it after it finished airing, but I don't know why. Usually jokes poke fun at the screaming in the show, but that doesn't even happen till the Freeza saga (over 40 episodes in). In fact, I think I enjoy the show more now than I used to (~8 years ago) because I can compare it to much more anime. For example, the battles in Bleach are dragged on much longer and are more ridiculous/annoying. And although most people won't believe this (because all they remember from the show is the screaming scenes): It's a very good show! There is a reason it gets amazing ratings in Japan. Kai is always on the Top 10 most watched anime in Japan, I don't get why it's not as loved here.
Animation is still the same as it was 20 years ago (wow! I didn't realize it that that old!), expect for touch ups. The opening/ending was the only thing that was completely redone. It would have been amazing if they re-did the entire thing, but this isn't a remake (although many people expect it to be; please don't start watching this thinking it is or else you'll be disappointed).
I like this show. I love the characters, who are farmilar, funny, and entertaining. I love the long, over-the-top-action-packed battle scenes (although these types of scenes bother me in other shounen series). I'm rarely annoyed when a battle goes on for longer than it should. And I love the story, which took a martial arts anime and turned it into a sci-fi/martial arts series (which seems like a bad combo), and make it work very well. There are a few battles (Freeza) which still last a bit too long, and it does slow down the show, but overall it's not too bad.
I was expecting a few more upgrades from the original, but I can't judge it based on what I expected. As it is, it's a great show and I recommend it to all shounen fans! If you saw the original (or even if you didn't), I would recommend this show.