Carrying capacity is the maximum sustainable population of a species the environment can sustain for an indefinite period of time given available resources. This is the point where the population theoretically cannot grow any larger and it is not growing any larger.
For functional purposes, carrying capacity will typically be an upper limit, but certain circumstances can temporarily take a population above this (though the population will decrease sharply thereafter).
Carrying capacity is determined and affected by a number of variables. The total geographic space available to a species determines the population number, but so does the amount of energy available for that species to consume. Interactions with other species, including humans, will also affect carrying capacity.
Carrying capacity can be increased by the amount of food available, the local extinction of a competitor, an increase in species fertility, a decrease in predation, an increase in the amount of habitat available for use, and adaptations to the environment, such as resistance to disease or adaptations that serve to decrease the amount of energy spent on obtaining food.
Carrying capacity can be decreased by disease, an increase in predation, hunting or harvesting by humans, a decrease in available habitat such as habitat destruction by humans, parasites, competition with another species for a resource, or changes in the weather that make the species less suited to the environment.
A similar question was answered here in the calculus section of Socratic.