Ok this little beauty is a must have for any ds owner. I got mine 1 year ago now. Basically this little cartridge enables you to play NDS roms and homebrew software on your ds. Now these are made legally for homebrew software only but everyone uses it to get free DS games from websites like romulation, nds-roms ect. The R4 is the same size as a ds cartridge only it has a tiny slot at the top of the card where your small micro sd card goes. Now when you buy your r4 it comes with a USB stick where you micro sd card goes on. This is where everything is stored such as games and homebrew. The setup is easy once you have got the hang of it. You can fit a lot of games on an micro sd card. I have a 2gb and i can fit 28 ds games on there and 25 gba games but you need an expansion pack for gba.
I thoroughly reccomend this gem. there are many other carts out there a and the R4 is old but reliable. Buy from a safe place because some are bricked which means they are fakes and will break your ds or just wont work.
Here is a website that has a guide on how to set one up: http://www.wikihow.com/Play-Roms-on-a-Nintendo-DS
Definitely get one peeps but remember downloading roms is illegal unless you have an original copy. Homebew is all good though. This website is great for homebrew software and help: www.gbatemp.net.
P.S. The R4 is not compatable with the DSi. Nintendo thought that one well through for once.