In FINAL FANTASY XIV, the standard measurement of in-game time is called Eorzea Time (ET).

Some content changes according to in-game time progression, such as the availability of certain fish or unspoiled gathering points. Players may also find it useful to reference Eorzea Time when coordinating for time-dependent challenges like FATEs and the Hunt.

Displaying Eorzea Time on the HUD
Local time is displayed by default on the HUD. To switch to Eorzea Time, select System > Character Configuration > UI Settings > HUD and click the box labeled "Eorzea Time" under the category "Clock Type."

You may also click directly on the HUD time display to change what time is shown.

See Basic Information for more details.