The Familiars are Avatar pieces which can be bought with Favour points. You can try on or purchase Familiars from the Avatar Shop page, as well as purchasing a Familiar for a friend. They were first introduced in March 2010. 
Once a Familiar is bought you gain a permanent stat bonus, regardless of whether or not the Familiar is equipped without losing the boost. Once you buy a Familiar, you can also buy the next level Familiar in the set. Each Familiar is equipped in the Familiars Slot on the Avatar page for a limited time. There are currently 35 sets with 3 spirit animal companions per set.
Mythology and Etymology
A familiar or familiar spirit is an animal-shaped spirit that serves for the purpose of sorcery or other supernatural means. Familiars serve their owners as domestic servants, farmhands, spies, companions, and may help bewitch others. Familiars are considered an identifying characteristic and are most heavily associated with early English witchcraft.