Definition

The polar night jet is a Jet Stream that forms high up in the stratosphere above the pole (at around 60 degrees latitude) during the Polar Night (during the winter when there is no sun in the polar regions). 

Description

During the dark winter months, the air high over the poles becomes much colder than the air over the Equator. This difference in temperature gives rise to extreme air pressure differences in the stratosphere which, when combined with the Coriolis effect, create the polar night jets that race eastward at an altitude of about 30 miles - in the upper stratosphere and mesosphere. 

These winds should not be confused with the Polar Jet Stream that develops below in the troposphere.

Relationship with the polar vortex

The polar vortex is circled by the polar night jet. The warmer air can only move along the edge of the polar vortex but not enter it. Within the vortex, the cold polar air becomes increasingly cold, due to the lack of  warmer air from lower latitudes as well as a lack of energy from the Sun entering during the polar night.     

Typical polar vortex configuration (source:NOAA)