What does it mean by a "research university"?
In the US, the Carnegie classification is used to describe different kinds of academic institutions. The system  changed in 2005, but under the previous incarnation, universities that had significant research components were called "R1" universities. Under the new system, universities with research components are called "RU/H" or "RU/VH" (Research University/(V)ery (H)igh research). It's most likely that the term 'research university' is an indirect reference to this. 

Update: The Carnegie classification has many categories of institution: only three of them are predominantly research-focused. So there are many more "non-research" institutions than there are research institutions.