The principle Buzzbox describes is correct, with slight number changes in between airframes.
Essentially what you are doing is using the actual weight of the aircraft and using only the amount of thrust required for that weight to depart rather than the full engine rating on each departure.
Selecting a lower rating as part of preflight (reducing your engine output for departure) automatically tries to achieve later on reduced climb performance as well.
The reduced engine thrust is still capable of performance capabilities required for obstacle clearance gradients, so no safety issues regarding performance are an issue here.
Thus manufacturers propose it as a fuel reduction technique for departures using a combination of both fixed derate and assumed temperature method (Boeing), increasing engine EGT margins and prolonging engine lifecycle.