This is a really good question, and some will ask what's still the same. Obviously Apple has given some information on it's website that I'm sure you've seen.
For me the most important feature is the 512Mb of RAM which is used by the programs it runs. The iPad 1 only had 256Mb. For two programs at once you might need twice as much memory if both use the maximum amount. It also has two processor cores now, so each core could run one program. The graphics chip has been upgraded to work faster and this will help produce better more realistic games.
Next it has two cameras, one on the back and one on the front. Those are needed for FaceTime video chat, a sort of video messaging, and of course for taking pictures.
Remember when you needed a cover or a case to protect the screen? Well now it comes with it's own and that folds up at the back to make a stand or to prop it up for typing. You can also choose what colour you want for the cover. Physically it's slightly thinner and and lighter. You can get it in white as well as black. I believe it's slightly cheaper than the first one but VAT has gone up so that needs checking.
The video output can now be HD, High Definition like Blue Ray DVDs, but you have to buy the connector for that.
So Apple have made some really good improvements here. Best to wait a while if you can to see if there's any problems with the new hardware. Some people have said there's some light leaking around the edge of the display, so that's one to watch.