The PCT is the Pacific Crest Trail, or more specifically the Pacific Crest National Scenic Trail. The actual lenght is supposed to be about 2663 miles before detours due to fires and endangered species needs. There are a few unofficial route options as well but generally it is a hike along the crest of the mountains in California, Oregon and Washington from the Mexico Border into Canada. There are other similar hikes like the CDT (Continental Divide Trail), AT (Appalachian Trail). If you do all three you are said to have done the Triple Crown.
Most people hike North starting near Campo, California. The finish is at Manning Park, BC, Canada.