A Video Card plugs into the Motherboard, and you plug the Monitor into it.
There's 2 main types, AGP {older} or PCIe. Depends on your motherboard as to which is compatible with your system. They are both easy to install.
It has it's own GPU - Graphic Processing Unit, and it's own RAM, thereby freeing up a bit of your System Resources, but all the power is in the GPU.
Onboard is OK for Office type applications, and very basic Gaming - like Chicken Invaders.
Vid Cards range from basic $60 models right up to $1000. What you buy is dependant on your usage {and your bank balance!}. A lot of people {me included} go for a Mid Range Card which delivers good performance and doesn't require a 2nd Mortgage. Something like a 7600GT, X1950 etc won't cost the earth, yet has good performance.
I hope this helps {It's early morning here, need more Coffee!}