Without getting into the technical jargon of digital image reproduction, knowing the general difference between these two types of images is important.
Basically, bitmap images are defined by pixels, dots within a certain amount of space. Depending on the pixel count per inch, the image quality can vary greatly. Bitmap images lose quality if they are reproduced at a larger size. When you zoom in to a photograph you will begin to see the pixels.
Vector images are a different technology. These are created for print reproduction, for a crisper look. The quality of the image stays the same when you increase or decrease their size.
However, bitmap images can be created at a very large pixel count with print production in mind. If scanned at a high dpi (dots per inch) than it is often fine for print.
Although vector images do create a much crisper line, the problem from an artistic standpoint is that the artist’s line becomes generic.
More should be said about this because it’s not quite that simple. This is just a very brief intro to the topic.