The 23rd century is the century of the Christian Era or Common Era which, in the Gregorian calendar, begins on January 1, 2201 and ends on December 31, 2300.
Unless changes are made in the religious calendar, in 2285, the Western Easter will fall on March 22 for the first time since 1818, the earliest possible date on which Easter can occur.
See Eschatology: Judaism.
The majority of Star Trek and the first six movies are set in the 23rd century.