Normally, an aircraft will have a certified maximum take-off mass (MTOM). For specific operations, military aircraft can be authorised to operate at greater mass within certain carefully defined criteria.
However, in peacetime, MTOM may not be the maximum mass which meets scheduled perfomance limits, either because of a short runway, high OAT, partial unserviceabilities etc. When all criteria are taken into account, the result is the 'Regulated' Take-Off Mass.
To take an example, although the French Concorde which crashed was probably below its MTOM, it was well above its RTOM - hence it was operating illegally from the moment of brake release. Not that you'll read that in the DGAC accident report....