In such fields as agriculture or horticulture, selective breeding was the process by which specific plants (such as flowers) or animals (such as livestock) were selected for breeding purposes to produce offspring with desired traits. The breeding stock were those specifically selected for breeding.
In humanoids, extreme cases of selective breeding was known as eugenics, which according to Spock, the Eugenics Wars on Earth was mankind's "attempt to improve the race through selective breeding." (TOS: "Space Seed")
In 2254, the Talosians lured the USS Enterprise to Talos IV to find a mate for the lone crash survivor Vina who had lived on their planet for the previous 18 years. Vina's attraction to the alluring Captain Christopher Pike made him a "prime specimen" for the Talosian needs. (TOS: "The Cage") Upon reviewing the events of that time, 13 years later, Commodore José I. Mendez asked then Fleet captain Pike if he was "captured as breeding stock," to which Pike concurred, leading Captain James T. Kirk to wonder if it was just in order "to maintain a supply of zoo specimens?" Spock, explained that it was "much more." (TOS: "The Menagerie, Part II") When it appeared that Vina failed at seducing Pike, they allowed for Number One and J.M. Colt to beam down from the Enterprise in order to produce the offspring the Talosians desired to create the Human slaves, later analogized to Adam and Eve, they desired to breed. According to The Keeper, "Each of the two new specimens has qualities in her favor. The female you call "Number One" has the superior mind and would produce highly intelligent children. [...] The other new arrival has considered you unreachable but now is realizing this has changed. The factors in her favor are youth and strength, plus unusually strong female drives." (TOS: "The Cage") Ultimately, neither were immediately selected, until Pike was finally able to join Vina in 2267, after he had no other means of survival following an accident. (TOS: "The Menagerie, Part II")
The colony on Omicron Ceti III originally had a number of animals brought along on the expedition that were along "for breeding and food purposes." By the time of the arrival of the Enterprise at the planet later in 2267, it was found that none of them had apparently survived. (TOS: "This Side of Paradise")
Cyrano Jones maintained his tribble stock in 2268 by removing them from their natural habitat, noting that "Breeding animals is not against regulations, only breeding dangerous ones. And tribbles are not dangerous." (TOS: "The Trouble with Tribbles")
Provider 2 believed that the inclusion of the "new blood" of James T. Kirk, Nyota Uhura and Pavel Chekov "would stimulate our stock of thralls." He was, however, wrong, and deemed it necessary to "destroy" the newcomers. (TOS: "The Gamesters of Triskelion")
It was the observation of Captain Jean-Luc Picard that the Mariposans, a colony of clones, needed "an infusion of fresh DNA" because "in fifteen generations" they'll cease to exist, and since "cloning isn't the answer. What they need is breeding stock." This led to his suggestion of having the Bringloid be that very stock they need. (TNG: "Up The Long Ladder")