A video card is enhancement card that usually plugs straight into one of the enhancement slots on the Motherboard. The monitor plugs directly into the video card. The video card takes the digital signal and changes it to an analog signal for the monitor. Today most video cards are equipped with their own memory, called VRAM or video ram. A good video card can have up to 64MBs of memory dedicated just to displaying graphics or 3D material.
Some video cards have their own chipset and memory.
We have two in the CS department. They have the capability to hook a monitor off of them so while the crowd is watching your presentation on the big screen you can be sitting at a normal monitor working the mouse. They usually don't have a real high resolution capability. You can also hook up television or VCR's to them. In the summer I take our's home and have a drive-in movie party in my backyard, I shine it on the back of my house.