Lift opposes weight and drag opposes thrust.
Generating lift causes drag.
As weight decreases (fuel is burnt), the amount of lift required is reduced.
Therefore the drag is reduced.
If nothing is done, the aircraft will speed up.
Very broadly speaking, with jet engines the higher one goes then the more fuel efficient the engine.
There will be a certain altitude where with all the above forces, the speed is at the most efficient speed for the aircraft / conditions and the engine is operating at it's most efficient setting i.e you are getting the best from the aircraft.
As fuel is burned weight decreases and as I said above the drag decreases meaning that the amount of thrust required to maintain the ideal speed is less. However, if you throttle back then the engine is no longer operating at the most efficient setting.
The ideal answer is to maintain the same speed and the same ideal power setting but using the now excess thrust to (slowly) climb the aircraft.
Since fuel is constantly being burnt then weight is constantly decreasing so there is a continuous excess of thrust required which is used to climb the aircraft.
Thus the perfect way to operate a jet aircraft is the cruise climb technique as described.
In practice most flights can't do that due to ATS restrictions and will compromise by using step climb i.e. initial climb to perfect level and cruise at that level for longer than it efficient until the weight is low enough to climb to the next level where the process is repeated.
There are 100 other factors involved but the above is a brief rounded explanation of the "cruise climb technique".
Regards,
DFC