The Federal Aviation Regulations or FARs are broken down into different parts. These parts are made up of a series of regulations pertaining to specific topics. Within those parts there are subparts which get more specific.
Part 61 deals with the certification of pilots. More specifically, it lays out the requirements for each certificate and rating, currency, flight reviews and so on.
Part 91 can be thought of as general operating rules. All aircraft are subject to these rules. Examples from this part would include the pilot in command's responsibility, inoperative equipment in the aircraft, specific VFR and IFR rules. IFR rules such as landing criteria, alternate airports and so on.
Part 121 pertains to the airlines or more specifically, air carriers. Scheduled passenger service (and some frieght like FedEx) follow part 121. Examples from this part include rules about flight attendants, cabin baggage, and general operating procedures.
Part 135 is the "on-demand" flights. These would be charted jets, small passenger service flights, small freight flights.
I hope that I answered your question.