Maximum takeoff weight

The maximum takeoff weight (MTOW) or maximum gross takeoff weight (MGTOW) or maximum takeoff mass (MTOM) of an aircraft is the maximum weight at which the pilot is allowed to attempt to take off, due to structural or other limits. The analogous term for rockets is gross lift-off mass, or GLOW. MTOW is usually specified in units of kilograms or pounds.
MTOW is the heaviest weight at which the aircraft has been shown to meet all the airworthiness requirements applicable to it. MTOW of an aircraft is fixed and does not vary with altitude, air temperature, or the length of the runway to be used for takeoff or landing. 
Maximum permissible takeoff weight or "regulated takeoff weight", varies according to flap setting, altitude, air temperature, length of runway and other factors. It is different from one takeoff to the next, but can never be higher than the MTOW.
Certification standards.
Certification standards applicable to the airworthiness of an aircraft contain many requirements. Some of these requirements can only be met by specifying a maximum weight for the aircraft, and demonstrating that the aircraft can meet the requirement at all weights up to, and including, the specified maximum. These requirements include:
At the MTOW, all aircraft of a type and model must be capable of complying with all these certification requirements.
Multiple MTOW.
With several of the manufacturers of large aircraft, the same model of aircraft can have more than one MTOW. An operator can choose to have the aircraft certified for a reduced weight, often for a reduced cost with an option to later increase the MTOW for a fee and the cost of certification change. Some airlines which do not require a high MTOW choose to have a lower MTOW for that particular aircraft to reduce costs (Landing fees and air traffic control fees are MTOW based).
In other examples an increased MTOW option is achieved by reinforcement due to additional or stronger materials. For example, the Airbus A330 242 tonnes MTOW variant / A330neo uses Scandium–aluminium (scalmalloy) to avoid an empty weight increase.
Smaller aircraft like the Cessna 208 Caravan may have an option for a reinforced undercarriage to permit an increase in MTOW.
Maximum permissible takeoff weight or maximum allowed takeoff weight.
In many circumstances an aircraft may not be permitted to take off at its MTOW. In these circumstances the maximum weight permitted for takeoff will be determined taking account of the following:
The maximum weight at which a takeoff may be attempted, taking into account the above factors, is called the maximum permissible takeoff weight, maximum allowed takeoff weight or regulated takeoff weight.