This is the amount of hours difference between your server time and
UTC/GMT (Greenwich Mean Time). It will correct your forum's displayed times to match UTC/GMT times. To provide the correct Time Zone offsets for your users, this number must be accurate.
Example: If your Server Time is currently 8:20 AM and the GMT is 2:20 PM, you would enter "6" in this box to add six hours to your forum times.
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EDIT:
If your individual user is having an issue with incorrect times when they are logged in, they can easily correct their user account's time display to whatever offset is needed, to get it matching their local time.
If you always wanted to just use your local server time for Guests, you would enter "0" in the admin CP time offset box. Then let your users offset their own times, in their My Stuff > Site Preferences, based on your server's time.
Be aware though, if you have users who have adjusted their time offsets, and you then change your site time offset (from the admin Control Panel), all your user's times will be based on that new time.
