The censors took a regular census of the Roman people and then of apportioning the citizens in voting classes on the basis of income and 'tribe' affiliation. Tribes in the Roman state were not ethnic but assigned by the censors - only the descendents of ancient citizen families considered themselves related to their tribe by blood. The censors enrolled new citizens in tribes and voting classes as well - slaves who had been freed since the last census automatically entered citizenship.
The censors were also in charge of the membership roll of the Senate, adding new senators every five years who had been elected to the requisite offices. After the Sullan reforms of 81 B.C. new senators were enrolled automatically, much reducing the influence of the censors over membership in the Senate.
See Roman Republic, cursus honorum
Today, censor is usually understood to mean any person who oversees a list of approved or disapproved works of writing or the other arts.
See censorship