Nvidia cards are more suited to drawing games, that's why. CUDA of course is their little alernate processing method technology that's basically to accelerate things that no other card can. Like if you have Nero 9 I think it is and you're burning a DVD, it will render the frames with CUDA instead of your CPU and you'll be done in 20 minutes instead of 60 minutes. Or in photoshop, you can run a noise reduction filter based on CUDA using the graphics card to calculate the pixel changes basically instantly when your CPU and RAM would have taken maybe 10 seconds to do it on a super high res photo.
CUDA happens to be slightly better at mining too, like 25-50% better in most cases so if you want to try it out, just get a miner and run it in CUDA mode and if it fails, you're missing something. Technically you don't have to install CUDA itself but it is included as an optional component in the Nvidia drive (but installed by default unless you choose custom and tell it not to). So just go grab the newest Nvidia drivers, choose custom when it asks what installation type, make sure everything on the list is checked, and hit go and you'll have CUDA capabilities.