Zero no Tsukaima, or The Familiar of Zero as it is known in the west, is a fantasy comedy-romance anime that tells the story of a young female mage named Louise Françoise de la Baume le Blanc de la Vallière, the main protagonist. Louise is the third daughter of a aristocrat family (La Vallière) and attends to the magics school of her kingdom, Tristain. As the first exam of her second year of her magics studying, she is supposed to summon a familiar, a creature that will be loyal to her and accompany her for the rest of her life, protecting and guarding her, but Louise is not very bright when it comes to magic casting, from where she gets her nick name: Zero Louise, as in zero accuracy Louise. A series of events unfold as she casts her familiar being, Hiraga Saito, a human that came from the "real world", Japan. Other students summon creatures like: a dragon, a firespitting salamander, a beholder, etc., aggravating poor Louise's situation and popularity in school.
The society in Tristain and the neighboring kingdoms is organized in a simple way: whoever comes from a rich family and is able to cast magic is called an "Aristocrat", the rest are called plebeians, after the ancient/medieval times society in Europe.
Doesn't take long for Louise to realise that Saito, her plebeian familiar, is special in many ways for her as he starts becoming popular in school and learn to master his newly acquired abilities, which will be very valuable for the upcoming dangers and war plots that they will face.
Note: Anime is different from the novel. Some of the time line for the novel have been rearranged in the anime version. Some stuff has been added and/or left out. Like a lot of book to film.