A number of factors are involved, along with some background to set the picture.
In level flight the aircraft has a certain weight acting towards the centre of the Earth which must be countered by an equal but opposite force called Lift. Lift is produced by moving an aerofoil through the atmosphere which causes the air to be deflected downwards resulting in an opposite reaction.
The reaction can be divided into two components: Lift, acting opposite to Weight, and Drag, acting opposite to the direction of flight. Nothing is free and Drag is the cost of producing Lift caused directly by the Lift production and also just the act of shoving the airframe through the air.
In order to maintain the forward motion producing Lift then a force (Thrust) acting equal to and opposite to Drag must be provided. Hence the need for some sort of engine shoving air backwards to produce the desired opposite reaction forward. That requires fuel.
As it happens, Drag is at a maximum at low speed, reduces to some minimum as speed increases, then rises again until there is no more Thrust available to make the aircraft go faster. So, there is a speed where Drag is at a minimum for the Lift being produced, thus requiring the least amount of Thrust from the engine, and, for piston power, that is the speed that will result in maximum range ie the equivalent of best miles per gallon in a car.
Of course one would also need to ensure that anything that unnecessarily increase drag are kept in in their lowest drag configuration eg gear up, flap up, minimum weight (more W = more L needed = more Drag = more thrust required = more fuel burnt).
A normally aspirated piston engine is most efficient - thus will be able to produce its maximum power) with minimal obstruction interfering with the airflow through the engine. A throttle reduces the power the engine produces by restricting the airflow through the engine. It really does throttle the engine, no different to someone with their hands around your neck. Also its fuel flow is approximately proportional to the power produced.
A normally aspirated engine produces more power when the air is dense. Less dense air means fewer oxygen molecules to match to the fuel. The atmosphere becomes less dense with increasing altitude so normally aspirated engine experiences a reduction in max power available as the altitude increases. At low altitude it produces more power than is needed to produce the Thrust required to counter Drag produced at the speed flown and must be throttled. That has an adverse effect on efficiency.
To maintain power as altitude is gained the throttle must be progressively opened. At some point the throttle will be fully open and the engine will be at its most efficient.
So, the upshot is that the airframe must be flown at the airspeed that produces the least amount of drag and at an altitude high enough that the throttle must be wide open to produce the power needed to maintain that airspeed.
NB: I've ignored leaning and centre of gravity considerations