The Purpose of Motherboard Onboard Video
Motherboards have onboard video so that you do not have to buy a separate graphics card in order to have video and graphics on your PC.
Desktop PCs without onboard graphics
A video card/graphics card will go into an available PCI or PCI Express slot on your motherboard. From there, you can plug your monitor into the graphics card, allowing your PC to display graphics on the screen. For example, on a desktop PC without onboard graphics, you connect the monitor to the back of the PC via a graphics card.
Desktop PCs with onboard graphics
If you have a desktop PC with onboard graphics, you can connect your monitor to your PC via the onboard graphics, directly into the motherboard.This is a feature that isn't really noticeable without opening up your PC. Both onboard graphics and graphics cards use connection types such as VGA, DVI, and HDMI. Onboard graphics basically means that your motherboard has built-in video processing capabilities; no video card or graphics card required.
Laptop PCs with onboard graphics
Onboard graphics are highly popular on laptop motherboards. Why? To save space. A graphics card takes up quite a bit of room, and because today's laptops and netbooks focus on being ultra portable, there is simply no space inside for a large graphics card or video card. Thus, computer manufacturers use motherboards with onboard graphics to display video on the laptop screen.
PCs with both onboard graphics and video cards/graphics cards
It is possible for a PC motherboard to have onboard graphics capabilities and a video graphics card. Most of the time, onboard graphics are a bit limited, and may not have enough power for video intensive PC work and gaming. Thus, many people choose to add a video card as well, in order to add more video processing power to their computers.
See both pictures below to see an example of onboard video vs. graphics card video.