The clock in the game displays EVE Time, which just happens to be in perfect sync with GMT. This article explains what EVE Time is, how to convert to your local time and why you should use it.
Some players will call EVE Time 'ET', but make sure this is not mistaken for Eastern Standard Time. This is usually abbreviated to EST, but some people mistake ET to mean 'Eastern Time'. Also, GMT and UTC (Universal Time Coordinates) are one and the same.
The clock in the game can only display ET and not your local time. Many players ask why they can't change it, but it actually makes sense to use ET in the game. It helps to plan activities with other players from other timezones and prevents everyone from having to know all the timezones, their names and abbreviations. Everyone in EVE is on the same time: EVE Time.
GMT (and as such ET) has no 'daylight saving time', so it will remain the same all year, without leaping an hour forward or backward. This means the difference between your time and EVE time will probably not be the same all year. Use a webpage like the World Timeserver
to make the conversion if you are unsure.