The theory of r/K selection was the joint work of the ecologists E.O. Wilson and Robert MacArthur, who sought to propose a working hypothesis to explain how environmental and biological factors influence reproductive strategies. In short, r/K selection theory sets up a continuum between two diametrically-opposing poles: on one end, r-selected species reproduce frequently, with large litter sizes, and invest a minimal amount of resources in each individual offspring, while K-selected species reproduce infrequently, with litter sizes of one or two offspring at a time, and invest a large amount of time and resources into the well-being of their young.
r-selected species tend to be small in body size and are found most often in unstable, unpredictable environments. They often are prey species. Their strategy seeks to maximize the number of offspring (who are even more vulnerable to environmental stressors and predation) at the minimum expenditure of resources, so that at least a handful of young survive to sexual maturity and pass on their parents' genes. The phrase 'multiplying like rabbits' is particularly applicable here, because rabbits, being small prey animals, must have lots of little bunnies to perpetuate the species. However vulnerable each individual r-selected critter may be, they are, on the whole, able to bounce back quite deftly from environmental stressors, like cockroaches surviving a nuclear apocalypse. This is in part thanks to their large litter size and frequent mating, which increases the rate at which selection for beneficial adaptations may occur.
K-selected species tend to be larger in body size and are most often found in stable environments. They have few or no natural predators. Their strategy is to invest the most resources possible into the rearing of their offspring, who are few in number, and ensure that they have the greatest possible chance of surviving to sexual maturity. The great apes, elephants and cetaceans are the quintessential K-selected orders: they tend to take over a decade to reach sexual maturity, reproduce infrequently and have long lifespans (some exceeding a century). While the number of offspring rarely exceed the litter sizes of r-selected species, each individual offspring has a greater chance of survival to adulthood. However, K-selected species are particularly vulnerable to environmental stressors, especially the loss of resources in their natural habitats. This is why all the above-mentioned orders are endangered or at least threatened, thanks mostly to the actions of one particular K-selected species, Homo sapiens.
Some genera buck this trend, such as sea turtles, who enjoy fantastically long lifespans, but lay large litters of unprotected and unnurtured young. Glowing Fish points out that the cuddly and adorable water bear is also a K-selected species.