Your book is not very clear. It should have said that the passive voice in Italian consists of a form of essere plus the past participle of the main verb. In the car example, the main verb is riparare (to repair).
Let's start with the active form:
The car is in the garage now.
Adesso la macchina è nel garage.
The car has been two weeks in the garage.
La macchina è stata due settimane nel garage.
The car is repaired by Max right now.
La macchina è riparata da Max proprio ora.
The car has been repaired by Max two weeks ago.
La macchina è stata riparata da Max due settimane fa.
There is no stare (to stay) in your examples: stato, stata, stati, state are not only the past participle of stare, they are also the past participle of essere (to be).
- La macchina = the car
- è = is (but in English you say: has)
- stata = been
- riparata = repaired
Why does essere use the same past participle as stare? Because Latin.
The Italian past participle comes from the Latin perfect participle, but in Latin intransitive verbs had no perfect participle (exception: deponent verbs). This makes sense because in Latin the past participle is used only in passive sentences, and usually the passive form does not exist for intransitive verbs. In Italian (and in English!), though, the past participle is used for some past tenses, which made it necessary to assign past participles also to intransitive verbs and particularly to the active-only verb esse/essere (to be). So, the past participle for essere was borrowed from the verb of similar meaning stare (to stay); stare is also lacking most passive forms, but it does own an impersonal third-person passive form, therefore it has a perfect participle: the word status that several European languages are still using with the same spelling.