Of the tales of witches since the Early Modern period, the familiar spirit is probably the most intrinsic after the flight to the Sabbath. However, there is a lot of misinformation on what exactly the familiar spirit is and its purpose.
Many modern writers make the familiar spirit out to be some sort of animal spirit, or perhaps a physical animal. If one took a glance at the confessions of the witches and cunningfolk, one would see that this was not true.
In fact, if one would look through the testimonials, one would see that the witches made no mention of their attending spirits as physical animals, and it was rather those that -observed- the witches that claimed the animals were their familiar spirits.
So in my opinion (coming from a folklore based position), throw out the nonsense about a physical animal. The physical animal was murely a valuable worker in pre-modern people, especially those in Europe who had animistic worldviews like that of witches and cunning men. They can help in magick, but they aren't familiars. I refer to them as domestic helpers.
The familiar spirit, historically, is the spiritual doppelganger of the individual witch, a local spirit. It is, for lack of a better term, a reflection of the soul. It is the inner divinity, the spark of godhood, or however one wants to define it. The familiar spirit is the witch?s companion, lover, and assistant in magic. It is the fetch, the holy guardian angel of ceremonial magick, the faery lover of folk tradition. It evolved out of an animistic worldview.
The familiar spirit IS the witch, and yet is separate from the witch. The familiar spirit has its own consciousness, but it also part of the consciousness of the witch.
Feeding the familiar is by energy. There is a reason our ancestors left physical food and drink for spirits. Because they have energy, and the act of sacrifice is energy. Blood is also vibrant in energy for a spirit to feed upon. Lastly, and most relevant to the familiar, is sexual energy.
The relationship with the familiar spirits is largely sensual. Not necessarily intercoursic, but certainly erotic and sensual. This is because of what the familiar is. It is the witch, and the witch is it.
A book I'd recommend that is scholarly, is the book Cunning Folk and Familiar Spirits, by Emma Wilby. It largely has to do with the interactions between fairies (who derive from animistic world views) and cunningfolk/witchs and the connection to the spirit helpers of shamanic cultures outside of Europe.
It's quite a difficult read.