A climbing route is a trail that a mountain climber uses to go up a mountain. It is often simply called a climb.
Examples : D1 on The Diamond and The Nose on El Capitan are climbing routes.
The difficulties and lengths of climbing routes (as well as descriptions and photographies) can be found in books called climbing guides. For instance, en:Fifty Classic Climbs of North America is a climbing guide that describes climbing routes of North America.