The Nintendo DSi is the third interation of the Nintendo DS handheld. The console retains the slimmed down case of the DS Lite, with a few new added features. The biggest change hardware-wise is the addition of two 3 Megapixel cameras, one on the outside which faces away and one which is focused on the player. The Game Boy Advance cartridge slot has been removed (which means backwards compatibility with GBA games is now gone, (and as a consequence some of the 3rd party periphials that used the GBA slot are also not supported, such as Guitar Hero games, etc.) And of course, all DS flashcarts and the like are not compatible, but there are already compatible flashcarts being sold. On the plus side an SD slot has been added, also Ram and Processor speed has been upped as well.
The main selling point of the DSi over other DS models is the built in multimedia capabilites (hence what the SD slot is for, although I'm sure some enterprising hackers out there will find a better use for it.) Console comes with built in photo manipulation and music editing software, as well as internal wi-fi internet connectivity.
Is it worth getting? At the moment there are plans to produce software that is compatible across all DS models but would offer special DSi only features/modes. Eventually I suppose the plan is to phase out the earlier DS Lite altogether, although this may take a couple of years. The built in music/calendar/photo/chat software is pretty nice, but nothing I personally would use much. However I could see people of highschool or college age getting a lot of use out of it. Lack of backwards GBA compatiblity knocks it down some in my opinion.