The EU and the U.S. have about the same definition of rare diseases, and that is orphan drugs. Orphan drugs are for diseases that affect very small patient populations, fewer than one in 2,000. They're also severe, life-threatening, or progressively debilitating. For these diseases there's typically no treatments, so the goal is to actually be able to stimulate research and development because the cost of the research and development is as high as it is for any common disease, but the return on the investment can be very low because the numbers are small.
On December 10th, 2013. See this statement in context.