The average computer user probably isn’t familiar with vector graphics. These sorts of graphics are generally created in programs like Adobe Illustrator. The various lines, curves, and shapes are actually mathematical equations. What this means is that when you open the image in a program that reads vector graphics, you can enlarge it as much as you want. In “regular” images, the images get pixelated (fuzzy/blurry). This doesn’t happen with vector graphics. The most common use for these sorts of graphics is with logos.
If this is all new to you, then the best way to understand it is to try it. Download Squad recently linked to the Vector Magic online tool of the Stanford web site. This is an online tool that lets you convert an image into a vector graphic. You can visit the site and see samples. You can also try your own.