A video or graphics card is an expansion card that connects to the mainboard and generates the output to the monitor. It renders the image in the code that the monitor needs to display it on the screen.
Some prebuilt computers that you buy from large manufactures will have the video card on the main board.
The video card needs to have memory on it so that it can render and process the requests of the system. It usually has to send 60,000 frames per second to the monitor so that you see it a constant rate of speed.
An accelerated video card has some extra features built into it's code base that will help it render at faster rates or just make the image sharper. Some other special features enhance video.