A familiar has many terms. Like lark said a energy being. Or it could be a strap animal that teaches you whether this be a dragon lion tiger etc.. Or it could be a animal you share a spiritual bond with and helps you in your occult or magick.
I will say I have had a couple of curious incidences with my pets when Ihve been practicing magick both outside and inside. I usually put them in another room, but if they are sleeping I feel mean.
When tracing the circle astrall, my dog seemed to be able to sense the area, and walked around it, then sat in the eastern quarter. This was odd behaviour for him, he is never still if I am outside.
Could be coincidence, however, it was enough to temporarily distract me!
I personally do to see my dog as a familiar, the concept of it being a real animal seems outdated and very medieval to me. This again being said, I have seen a different term thrown around by few experienced authors and I was shocked to see them believe such things- I label it as nonsense still, but each to their own!
Aleister Crowley mentioned something about the spirit of an animal being an elemental spirit and that a magician could co-inhabitate the animals body and the animal, if given permission, would be glad with this and it 'elevates' the animals spirit....or something like that.
I am badly paraphrasing because I dismissed the idea, I am also struggling to remember where I read it- I believe it was in Liber ABA, but I do not have time to search through that book at the moment!
I prefer Aeon's definition, it is much more compatible with other people's personal paths.