I am reading Seutonious and he refers to certain characters as having been a censor. What is a censor. I get the impression that it was someone whodecided who was to be retained in the equestrian order and who would not based on the equestrians character. Is this correct?

http://ancienthistory.about.com/library/bl/bl_time_rome_censors.htm:
The fifth Roman king, Servius Tullius, divided the Romans into tribes, creating new ones in addition to the three original ones (ramnes, tities, luceres), and carried out the first census to distinguish the people into ranks based on wealth and property. After the dissolution of the monarchy, consuls took over the task of taking the census, and then in 443, a new magistracy was created to carry out the task of taking the census. In addition to serving as census-takers, these high ranking magistrates acted as censors dealing with morality, and were called censores.

The office was especially distinguished. Only the most respected of senators could hold the office.

I believe in the Imperial period, it was carried out under the auspices of the Emperor, and Augustus in the Res Gestae says he and Agrippa carried it out twice (maybe thrice) together.