Plain English Meaning
High up in the atmosphere, the wind in the middle of each hemisphere generally blows from west to east most of the time. That steady west-to-east flow is what 'prevailing upper level westerly winds' refers to.
Full Definition
The dominant west-to-east airflow found at high altitudes in the middle latitudes of both hemispheres, produced by the combination of solar heating differences between the equator and poles and the deflecting effect of Coriolis force on a rotating Earth. These winds are strongest in the upper troposphere and lower stratosphere and form the broad current within which the jet stream is embedded.
Context Anchor
Seen in weather theory and when explaining why many and tend to move from west to east across much of the .