Take the GE90-90B engine, its capable of producing 90,000 lbs of thrust, when its on the B777 the aircraft has a Max Takeoff Weight of 632,000 lbs.
If the aircraft is taking off at a lighter weight, it obviously doesnt need to use all that power. Using less power increases the engine life and therefore saves money for the airline.
The crew have two ways of reducing takeoff power, one is to tell the computers that the outside temperature is hotter than it actually is, (this is called assumed temperature) The computers will therefore reduce the amount of power available, there is a FAA limit on this power reduction of 25%.
The 2nd method is to Derate the engine, this is pretty much like saying you have a 81,000 lbs (-10%)thrust engine on the wing or even a 72,000 lbs (-20%) thrust engine. These are called Derate 1 and Derate 2, they are selected on the FMC.
You can combine the assumed temperature method with the fixed derate and therefore reduce your 90,000 lbs thrust engine by almost 45%.
Its pretty amazing when you consider that the takeoff is based on an engine failing at a point on the runway.