In common usage it means to be well known or close. There is an additional meaning, as anyone familiar with Dungeons and Dragons can attest. The obedient, magical servant of a witch or wizard. Inside the game's mechanics a players familiar is takes the static form of an animal, like a super powered pirates parrot, but in the folklore from which the idea springs the familiar was a shapeshifter. Sometimes an animal and sometimes a person and, most often, purely invisible, the familiar took whatever form it needed to stay around the wizard it was bound to, watching over him and breathing words of inspiration into his ear. Of course in the medieval days that this idea there was no such ideas as the wizard as we now imagine, with flowing beard, loyal army of walking brooms, and spell book arsenal filled to the brim with magic missile and prismatic spray. No, in those days the person who would have a familiar would be an occultist or alchemist. Someone attempting to unravel the secrets of nature. A genius, in other words, and what a word. Genius comes from Latin and originally meant a kind of spirit, one that is tied to a thing, or a place (then known as a genius loci), or to a person. Those of unique intelligence and ability were considered to have a particularly strong connection to their genius, one so strong that the spirit would whisper to them great ideas, until in time the word genius become associated not with the spirit but with the act of listening to one's own. And where did these genii, for that is the plural, come from? Some believed they were messengers between the gods and man. The Greeks had a name for such messengers, they called them daemons. Socrates in particular was known to have great knack for listening to his daemon.
Familiar, genius, and daemon. Each word double sided, meaning either a guardian spirit or the surprising, churning thoughts inside our heads, particularly those that come seemingly from nowhere and which tend to be our greatest. In the end whether these thoughts come from the invisible denizens of the ether or from the depths of our own subconscious is not so important, what really matters is that when people listen to the idiosyncratic voices buzzing through their minds they tend to become great, or sometimes mad, or often both.