When you're talking about what you can do with vector or raster graphics, it really depends on what you goals you're trying to accomplish with a particular image.
For instance, logos-- like this Prairie Dog logo I made that has to be used online, in printed format, large format billboards, etc.-- are commonly done in vector graphics. This is because vector graphics can be resized to a larger resolution without pixelation or loss of quality.
Raster graphics, like the Tom Brady background I made above, cannot be resized to larger graphics without losing a certain amount of quality. That said, with raster graphics you generally have more ability to do a greater amount of image effects. Raster graphics can generally be reduced to smaller sizes without losing quality, so if you're going to use raster graphics for a large-format design project it's imperative that you start and work with a greater image resolution that can be scaled down for smaller projects.
As far as what you can do with vector or raster graphics, it completely depends on the design software that you're using (and what version of that software as well.) In some cases, almost anything you can do with raster graphics can be done with vector graphics as well; in others, that might not be the case. It all depends on what you want to do, the software you're using, and how you go about designing your graphics.