Carrying capacity is the equilibrium or near-equilibrium abundance of a population. Population abundance grows, often very rapidly, when it is below carrying capacity, and it shrinks when it is above. Carrying capacity depends on such factors as resource supply, pathogen abundance, metabolic requirements, efficiency of resource capture and conversion, and resistance to natural enemies.
The concept of carrying capacity does not apply to very long timescales because populations evolve and diversify, with novel organisms being able to exploit previously unused resources. On evolutionary timescales there is no such thing as an equilibrium population size. The overall picture of the biosphere is one of expanding resource use and organism abundance.
Thanks to cultural evolution, human populations find ways to exploit new ecological opportunities on short ecological timescales. The short-term dynamics of human populations resembles the long-term dynamics of non-human populations. The concept of carrying capacity, as applied to humans, has no ecological basis. The same goes for the ideas of ecological footprint and sustainable development.