In GIS, vector and raster are two different ways of representing spatial data. However, the distinction between vector and raster data types is not unique to GIS: here is an example from the graphic design world which might be clearer. Raster data is made up of pixels (or cells), and each pixel has an associated value.
Considering this, what is vector vs raster graphics?
Raster images are made of pixels. A pixel is a single point or the smallest single element in a display device. If you zoom in to a raster image you may start to see a lot of little tiny squares. Vector images are mathematical calculations from one point to another that form lines and shapes.