What is "Operational Control"?
Operational control is defined in 8900.1 Volume 3, Chapter 25 as:


  Operational control functions include, but are not limited to:
  
  
  Preflight planning;
  For part 121 operations, preparation and dissemination of dispatch/flight releases;
  Canceling a flight due to potential hazardous or unsafe conditions;
  Ensuring that only those operations authorized by the OpSpecs are conducted;
  Ensuring that only crewmembers who are trained and qualified in accordance with the applicable regulations are assigned to conduct a flight;
  For part 121 operations, ensuring that no flight is started unless it has been authorized by a dispatcher or person authorized to exercise operational control in accordance with §§ 121.593, 121.595, or 121.597, as applicable;
  Ensuring that crewmembers are in compliance with flight and duty time limitations and rest requirements prior to departing on a flight;
  Designating a pilot in command (PIC) and, where applicable, a second in command (SIC) for each flight;
  Providing the personnel who perform operational control functions (PIC, dispatcher, etc.) with access to all necessary information for the safe conduct of the flight (for example, weather, Notices to Airmen (NOTAM), airport aeronautical data (analysis), and inoperable instruments and equipment);
  Specifying the conditions under which a flight may be dispatched or released (weather minimums, flight planning, airworthiness of aircraft, aircraft loading, and fuel requirements);
  For part 121 operations, ensuring that when the conditions, limitations, and authorizations specified in a dispatch or flight release cannot be met, the flight is either cancelled, delayed, rerouted, or diverted;
  For part 121 operations, ensuring that each flight is conducted in accordance with the conditions and limitations of the dispatch or flight release;
  Ensuring that each flight is operated in accordance with the limitations of the MEL and CDL;
  For part 121 operations, monitoring the progress of each flight and initiating timely actions when the flight cannot be completed as planned, including diverting or terminating a flight;
  For part 135 operations, locating a flight for which a Federal Aviation Administration (FAA) flight plan (FP) has not been filed;
  For part 121 operations, ensuring rapid and reliable communications in accordance with §§ 121.99 and 121.122, as applicable;
  Restricting or suspending operations in accordance with §§ 121.551, 121.553, or 135.69 as applicable; and
  Exercising the emergency authority described in §§ 121.557, 121.559, and 135.19, as applicable.
  


These functions are normally performed by a variety of people:


Dispatch
Crew Scheduling
Maintenance 
Chief Pilots
Director of Operations
The PIC of the flight
Manager of SOCC (System Ops Control Center)
Director of Training


Operational control is implemented by the above people and must hit all of the bullets in the definition above.  This means that to exercise operational control you must always know where your planes are, you must determine who flies them, plan those flights, ensure the pilots and aircraft are legal, ensure everyone is trained for the operations performed and to always be able to communicate with your aircraft.

There is also mention of Operational Control Systems, which require that any flight operated by the carrier is dispatched, followed and can be located at all times.  These functions are normally carried out by the Dispatcher assigned to your flight.

Further reading beyond the 8900.1 can be found in AC 120-101 for 121 ops.