Raster and vector are two different categories of graphics.
Raster images are composed of individual pixels of varying color that compose an image. Photographs are raster images. If you zoom in closely enough on any digital photograph, you will see thousands (and often millions) of pixels.
Vector images are not composed of individual pixels. Instead, vector graphics use lines and tones that are determined by coordinate points on invisible x,y axes. Curving lines always appear to be absolutely smooth at any zoom level. Many digital illustrations are vector images.
In printing, the important difference between raster and vector images is that raster graphics can only be printed or viewed at a certain size before they appear to lose image quality. The maximum size of a raster image is fixed, and nothing can be done to change it. It will look "blurry" or "jagged" when it's printed larger than its maximum size. Vector images, however, can be printed or viewed in an infinite array of sizes. You can never “zoom” in too close on a vector image to see it lose quality. The same vector image can be printed on a postage stamp or on a billboard and it won't lose quality.
If you have a photograph, it's raster and you're limited by its maximum size. But if you're designing a piece for printing that uses line art, a properly formatted vector graphic can go as big as you want it and will always look perfect.
