Plain English Meaning
An airway is a published highway in the sky. It runs in a straight line between navigation stations on the ground, and pilots use it as a known route to fly from one place to another.
Full Definition
A Class E airspace area established in the form of a corridor, the centerline of which is defined by radio navigational aids. Airways are typically 8 nautical miles wide (4 NM either side of centerline) and extend from 1,200 feet above the surface up to but not including 18,000 feet MSL. Low-altitude airways in the contiguous United States are designated with the prefix 'V' (Victor airways) and are based on VOR navigation.