From Wikipedia.org article:
Vector graphics or geometric modeling is the use of geometrical primitives such as points, lines, curves, and polygons to represent images in computer graphics. It is used by contrast to the term raster graphics, which is the representation of images as a collection of pixels (dots).
The human eye works as a bitmap picture: it catches the image in a mosaic raster of photon recipient nerves, a pixel image. But the brain - according to recent studies - handles it as a vector image. Perhaps because - like in our computers - this is easier to store. It explains why we can recognise simple drawings like cartoons with just outlines because this is so close to what our brain makes of the visual world anyway. It also serves as an explanation for the fact that logos and signs with easy and geometric shapes are easier remembered and recognised.
These are the three of the main issues to pay particular attention to when thinking about whether to use bit-mapped (also called "raster") or vector graphics.
Materials on understanding and using vector graphics.
Using only vectors, create an ad banner that would blend well into your first project.