Rules governing flight procedures during limited visibility or other operational constraints. Under IFR, pilots must file a flight plan and fly under the guidance of radar.
The set of rules that govern instrument flight. Filing IFR or departing IFR means that the pilot is operating under those rules. Aircraft are much more closely controlled under those rules and are permitted to fly through clouds as Air Traffic Control is keeping aircraft separated. To "be IFR" is to operate under these rules under a clearance from ATC. Sometimes pilots (including me) say IFR when we mean IMC, or refer to a field as "being IFR." When a field is IFR, it means that only departures and arrivals under IFR (or in some cases special VFR) are legal.
Rules governing flight in certain limited visibility and cloud conditions. Under IFR, an aircraft is required to be in contact with air traffic control facilities and is separated by ATC from all other IFR aircraft.