On a forum like this, and just about any computer forum, you will have people discussing video cards and acting as though they are a necessary part of a computer, but they aren't. Like a sound card, network card, USB port etc, a video card is an expansion card. It lets your computer do something that it wouldn't be able to do otherwise, but isn't required at all.
A graphics card is similar to your processor, in fact it IS a processor, but it just does it slightly differently, so it is better at the tasks you give it (shading, texture filling etc). Most onboard graphics on newer motherboards now will be able to stream HD videos without a problem, so you don't need a video card to watch HD videos.
The only time the need for a graphics card arises is if you are doing anything that needs specific graphical computing power. Gaming, CAD applications, rendering etc are what I am talking about. graphics cards are also better at doing what would seem to some people as a waste of resources, such as folding, which is simulating protein folding for medical research, then uploading the results to a single place (Stanford University).
Basically if you aren't gaming, creating and rendering 3D images (so not things like photoshop, they are 2D) or doing HD video editing, you have no need for a graphics card so long as your motherboard has onboard video. Only if you are going to do one of those tasks, or your motherboard does not have onboard video will you need a graphics card
