A map can be made up of many different layers. There is usually a base map layer to which all the other layers are added. Layer order is important to ensure that all layers are visible according to what you want your map to display. For instance, a raster layer over a vector layer could hide that layer's information. This problem is easily solved by reordering the layers so that all the appropriate data is visible.
Raster data requires far more storage area as it consists of a series of dots which can represent a scanned map for example. Any kind of scanned data is represented by a series of dots which, depending on the resolution, can be used in a number of ways. Raster can be used as a base map or as means of adding information as one of a series of layers within a map. For example, sea depth could be represented with a raster layer with each raster dot representing a sea depth.
When desk top GIS was first available, with the arrival of the personal computer, using raster data meant that maps often loaded very slowly. Also in the early days of the personal computer data storage was available in megabytes rather than gigabytes and was very expensive. Now computers are much faster and storage cost and size is no longer a problem. So using raster data, with super fast processing and gigabytes of storage, is a long way away from the problems of storing and displaying raster layers in the early days of desktop GIS.
So vector data is represented by x and y coordinates and can have database information associated with the point, line or polygons within the vector map layers. Raster data is represented by a series of dots and can be very detailed depending on the dot density. Unlike vector data desktop GIS does not link databases to this kind of data. Using both kinds of layer types can make your maps both meaningful and interesting for your own requirements and those of your clients.