These words are commonly confused and misspelled because their pronunciations can be extremely similar.
A censer is an object used to hold incense, usually with holes so the smoke may escape and sometimes on a chain to be swung during religious ceremonies.
To censor something is to remove content from media which is deemed to be hurtful or offensive. This is usually governed by a government or ruling body. A censor is someone who censors.
A censure (pronounced sen sher) is a criticism or judgement, sometimes from an official source. One may also be censured.