A cathedral is the mother church of a diocese. The name comes from Latin cathedra, meaning "chair" or "seat", and refers to the cathedral being the locus of the authority of the bishop of the diocese. This is expressed by his celebrating Mass on the church's high altar -many cathedrals have the cathedra behind the altar to emphasise this.
The cathedral of the Diocese of Rome is, and always has been, San Giovanni in Laterano. San Pietro in Vaticano is the focus of the expression of the Pope's universal authority, but is only the second in rank of the four major basilicas of Rome.
In Rome, there are a total of three cathedrals because the city's territory also includes much of the territory of the Diocese of Porto Santa Rufina and that (of limited extent) of the Diocese of Ostia:
Also, two very obscure ruined cathedrals exist (nothing is visible above ground):