Evolved from a grazing of animals perspective--how many cattle could you have on the range and keep the grass healthy?

Definition of Carrying Capacity:
Level of use in which unacceptable changes occur in the ecological and social qualities of a recreational opportunity.

There is no single carrying capacity for an area. Areas have multiple carrying capacities depending on the management objectives for this area.
Example--Yosemite Valley around the store has very different carrying capacity than the wilderness backcountry. We expect to have cars, lots of people in a grocery store. Most backpackers do not expect lots of people or impacts of people in the wilderness.