Familiars (使い魔, tsukaima?) are special assistants used by summoning-specialists. Since it's natural for a summoner to separate themself from society, the use of familiars capable of performing small, simple errands is considered orthodox. Although a different entity, familiars are seen as an extension of the summoner as there is both a mental and physical connection between the two. The symbol of the summoner itself and fundamentally different from regular, contract-bound creatures.
Nature
There are several ways to create a familiar. The most traditional is by placing the leftover thoughts of an already departed soul, of a dead person, into the body of a dead animal. Following that, the summoner needs to repair the animal corpse so that it can move again by using Reincarnation Ninjutsu. The resulting familiar will gain chakra thatand will be able to use various forms of ninjutsu just like the summoner. However, chakra cannot be produced independently and must be supplied by the summoner through their spiritual connection. Thus, a familiar requires a master to maintain both its powers and life.
This type of familiar will form its own personality and will be capable of reasoning and acquiring experience apart from the magus while sharing the same knowledge. Summoner's need something that has about the same level of rationale and reasoning, but can think independently. That way they can act as a teacher, and have the familiar be a teacher to them, too. It's better to discover new things that way, and it also makes it easier for them to realize their own mistakes. There is also a chance of the arising of abnormal powers. However, the presence of a personality also makes this type of familiar more independent from the summoner and many summoners really don't like that method. But some summoners make insurance by passing everything on to their familiars. Well, to explain it simply, it's a spare self that is a little behind on abilities. Important to note that this is by no means a form of resurrection, as the familiar is still a being completely different from the one whose chakra it received.
Additional notes
Familiars like the ones mentioned above can be made out of pretty much any creature: cats, dogs, birds, etc. Actual, living animals can be turned into familiars as well and summoners prefer this type more as other types since they are quick created and easily controlled by them. Humans can also be turned into familiars, but that is seen as a monstrous act and unpractical (due to the immense chakra burden) by most summoners. Also, familiars without souls can be used too, however the modern versions of these are weak.
Transfer of the master's consciousness into the body of regular familiars is possible and most summoners do so to remote control them while they are in recon or exploring missions. However, it is impossible to perform transfer of consciousness with a familiar that has its own soul and personality. In this case, the best that the summoner can hope for is sharing of senses with familiar (like receiving a video-feed of everything that the familiar sees and hears).
While it is possible to transfer one's consciousness/soul into a creature with an existing soul, this is nearly impossible. Even transference into a familiar without a soul doesn't mean that the summoner has completely transferred themself. Destruction of the body (this also includes through natural means like aging) of the summoner will mean the destruction of the soul of the summoner.