In ecological equations the letter K represents the carrying capacity of a given environment, and so it is also used to represent a species whose reproductive strategy is to keep a stable population as close to the carrying capacity as possible.
Some species who use this strategy are large mammals such as elephants and whales, primates such as humans, and many large birds such as tawny owls.
K-selected species tend to live in stable environments. They produce few offspring, that develop slowly and require a lot of care. They also tend to have long life spans.
Also known as equilibrium species, or K-strategist
Compare this reproduction strategy to r-selected species, (AKA big bang reproduction and opportunistic species). These have as many offspring as possible, and usually do not provide much care for their young. they tend to have short life spans, sometimes not living past mating (think insects).
Both r-selection and K-selection are comparative terms; you can think of them as indicating the end points of a continuum. Modern humans, often with only 2 children per mated pair, are an extreme case of K-selection, while many insects, such as fruit flies, could represent the r-selected end of the spectrum. Most animals will fall somewhere in between. For example, cats are r-selected compared to humans, and K-selected compared to cockroaches.