How can carrying capacity affect populations?
Carrying capacity effectively determines how much population a given region can support. It will act as an upper limit on the population size.
In general, however, for purposes of a logistic growth model, one can consider the carrying capacity to be an asymptote for the logistic growth function. Specifically in the case of a constant carrying capacity, if one's independent variable (time usually, though sometimes resources or the like) is on the "x" axis, and one's dependent variable (in this case, population) is on the "y" axis, the carrying capacity will be a horizontal asymptote parallel to the x-axis, and will represent a population level that the growth model will typically not reach.
Of note is that certain drastic circumstances can push a population over the carrying capacity (one of the more common examples being the sudden introduction of a large number of new specimens of the population). In these cases, the population tends to rapidly decrease, plunging back below the carrying capacity (and in many cases, even decreasing below the original number).