The term "hybrid" denotes a cross between two "types", and "types" can mean species, subspecies, races, breeds, or even down to a single trait. The idea is that at the level at which the discussion is concerned, "pure" refers to individuals of the same "type" which, if bred together, will have offspring of the same "type" (again, with respect to the level of "type" being discussed). A "hybrid" is the offspring of two different "types". Taxonomy deals with "types" as species or subspecies as the (generally) basic level. Genetics looks at individual traits (which may differ because of one genetic difference, more than one, or a suite which show degrees of expression, etc.) In chickens (and other domesticated animals and plants), the basic level can be "breed" (a group maintaining a shared general appearance, superficially similar to a species, but the result of exaggerating strongly-expressive individual traits), or like in genetics, with respect to specific traits within a breed (such as crossing a black and a self-blue of the same breed -- the offspring would be black hybrids heterozygous for self-blue).
In taxonomy, a hybrid would refer to a cross between two species most often, sometimes also between subspecies of the same species. Offspring typically look like something in-between their parents, and if they are also fertile and allowed to breed among themselves, offspring will show varying degrees of each original parent species -- thus, they won't "breed true" to either species with regards to physical characteristics.
In genetics, a hybrid refers to a cross between two different homozygous traits, or between two pure-breeding strains. One example would be the foundation of genetics, the studies of Gregor Mendel. He crossed different pure strains of peas, and the offspring were hybrids -- same species, different "types" with respect to specific traits (green versus yellow pea color, wrinkled versus smooth pea texture, tall versus short pea plant, etc). Since peas tend to self-fertilize without interference, hybridizing required manual transfer of pollen from one to another which had been emasculated. The offspring, if left to self-fertilize, would then beget offspring which were not all the same with respect to the specific traits observed -- thus the crossed peas would be called "hybrids" because they wouldn't "breed true".
In chickens (and also in many plants raised from seeds), buying hybrids means that the individuals had parents of two different "types" -- breeds in the case of chickens, or inbred strains in the case of seeds. The first-generation cross results in a general uniformity among the offspring, to the extent that you might think they were a pure breed or strain. But if they were left to breed among themselves, their offspring would be variable. And hence the term "hybrid" -- they don't breed true. The reason the first-generation hybrids are so generally uniform is because of a balancing of homozygous dominant and recessive traits from the different pure parent-breeds into straight heterozygosity in the hybrid offspring. They're uniform enough that one might think they actually are a "breed". But because the first-generation hybrids (F1) are heterozygous, the individual traits would segregate in new combinations in the second-generation hybrids (F2) non-uniformly. If you want to create a pure-breeding new type of chicken combining traits of two (or more) different parent breeds, you'd have to keep breeding the hybrids together until you 1) find what you want, and 2) get them to the point that all their offspring ALSO have what you want. In effect, you are making a new combination of homozygosity for the traits you desire. Until then, chickens with mixed ancestry that are very variable between their siblings are not generally called hybrids -- they're "mutts" or "mixed-breeds".
The point is that the term is used to represent crossing two different types. What that type is will depend on the context of discussion.
