Suppose your engine is leaking or burning oil but noticeably or only at higher rpm, why would higher rpms exacerbate leaks or burns?
The higher the RPMS (Revolutions per minute) the faster the engine is spinning and the higher the oil pressure gets in the engine, thus if an engine is burning oil due to a worn out rings or worn out seals for example. It would be burning a lot more oil due to the faster spinning pistons and the more bangs occuring burning the oil off.
If there was a leak, say a valve cover leak, more oil is going up there due to the higher oil pressure and thus the oil leaks. And as mentioned by other comments the higher temperature lowers the viscosity of the oil making it easier to get into the combustion chamber, hence why people with engines that burn oil use a higher viscosity oil