A polar vortex is a large-scale cyclone encircling the polar regions, that's the Arctic and the Antarctic. The shape of it changes when the adjacent jet stream meanders and grows in amplitude, creating Rossby waves. An effect is the transfer of cool high-latitude air to lower-latitude regions and warmer air to high-latitude regions. Another effect is more intense tropical cyclones and hurricanes.
Adapted from a deleted RationalWiki article