From Google's dictionary result, professional is defined as "A person engaged or qualified in a profession." This definition indicates that they should either actively be working in the field or be qualified to work in the field at a professional level of skill and conduct themselves in a professional manner (ie, good work ethic, morals, etc)
Personally, I define professional as a level of skill and training (which may be formal or self taught) combined with making money doing it. I know people who make their livings doing photography that I would not consider to be professionals based on their level of skill (or lack there of).
Alternately, I personally do not make my primary living as a photographer, however I do run a photography business and have a college degree that covers photography among other digital arts, so I consider myself to be a professional since I have both training, experience and regularly earn income (if minor) from photography.
As for the question of gear, I believe that it is possible to produce a professional level of work with gear that would normally be considered consumer grade, but it is also much more difficult and will put much more burden on proving your skill with a portfolio.