The CDT is a United States National Scenic Trail running 3,100 miles (5,000 km) between Mexico and Canada. It follows the Continental Divide of the Americas along the Rocky Mountains and traverses five U.S. states — Montana, Idaho, Wyoming, Colorado, and New Mexico. In Montana it crosses Triple Divide Peak which separates the Hudson Bay, Atlantic Ocean and Pacific Ocean drainages. The trail is a combination of dedicated trails and small roads and considered 70% complete. Portions designated as uncompleted must be traveled by roadwalking on dirt or paved roads.
The trail is one of 11 US National Scenic Trails and one of 3 that run a considerable section of the US North-South with the Pacific Crest Trail running from Canada to Mexico and the Appalachian Trail running from Maine to Georgia being the other two.
For those unfamiliar a continental divide is a drainage divide or basin that essentially divides the surface water(rain, snow melt, etc) between separate end points. In the case of the North American continetal divide surface water on the west flows to the Pacific Ocean and to the East it flows to the Atlantic ocean. So basically the divide plays connect the dots with the high points along the Rocky mountain range.
Though the divide runs though the high points the trail itself do not. An actual traverse of the divide would be an exercise in mountaineering rather than backpacking instead the trail attempts to follow the divide as closely as possible while remaining reasonable. As such there are many sections that are cross-country without trail. There is also flexibility to explore or take alternate routes, unlike the more defined Pacific Crest and Appalachian trails where there is a notion of a pure hike following the trail exactly. The CDT has no such notion, you are encouraged to 'Hike your own hike' creating your own alternatives, and scrambling up side-peaks. The primary rule simly being not to leave the divide for too long.