Vector graphics use geometrical formulas to represent images. Vector images have many advantages over raster images. Vector is resolution independent meaning you can resize 100x100 pixel image to 100x100 inches image without any loss of quality. That is not possible with raster images. In addition, images stored as vectors look better on devices (monitors and printers) with higher resolution, whereas raster images always appear the same regardless of a device's resolution. Another advantage of vector graphics is that representations of images often require less memory than raster images do.
More on vector vs. raster graphics on following links:
SignIndustry: Vector vs. Raster Graphics
Wikipedia: Vector graphics