Plain English Meaning
These are the air traffic control centers that watch over airplanes while they are flying high and far between airports, rather than near them. Each center handles a big chunk of the country's airspace.
Full Definition
Enroute ARTCCs are FAA facilities that provide air traffic control services to aircraft operating on IFR flight plans during the cruise phase of flight, primarily in controlled airspace between terminal areas. They manage traffic across large geographic regions, handing aircraft off between adjacent centers and to terminal facilities (approach and tower) as flights between phases. There are 22 covering the contiguous , Alaska, Hawaii, Puerto Rico, and Guam.