Why the spots in a rash?

My question is stimulated by our current Measles outbreak (and in particular by a picture frequently seen in our news of a rather miserable looking kid covered in spots), but it applies equally to any other disease that causes a rash.

In terms of what is going on in the skin and subcutaneous tissue, what IS a rash? I am puzzled why someone would get large numbers of spots rather than all of their skin turning bright red evenly.