Assuming zero knowledge of the term, familiars are animal companions for spell casters, often with greater intelligence, cunning, and comprehension. While the concept existed long before D&D, that game really brought the concept (as far as most gamers are concerned) into the light.
Depending on the ideas behind them, familiars can be little more than a smart animal or can be a magically potent ally, spy, and source of arcane information.
Insofar as the Dresdenverse, it is generally thought that familiars are non-existent. Little Brother had not exhibited anything beyond being a cool raccoon, and there is no major evidence that Mister is anything beyond a big, attitude-fueled cat.
That said, I think familiars definitely have their place amongst the magical community, whether it's a witch's black cat or Injun Joe's raccoon.
For my upcoming campaign, Librarian's of sufficient rank can gain access to an Athenaean owl, a Little Owl imbued with a fragment of Athena's insight and wisdom. Mechanically, I built them as an Item of Power, since that allowed the greatest amount of conceptual freedom along with a point mechanic that worked (things like It Is What It Is really resonated with the concept of a familiar, in my mind). Granted, it stretched the Item of Power's concept, but I'm not at all adverse to doing that for my own game (in fact, I've created several Items of Power that are "mass produced", at least as far as Items of Power are typically conceived of).
For those wanting a refresh-free method, CMEast's idea works, although that does little for a familiar's own motility or independent action, let alone the ability to target and affect them as their own entity.
Doc