Wikipedia's servers record activity based on Coordinated Universal Time (UTC for short). You can set your user preferences to display time for the time zone you are in.

If you do this, Wikipedia will show all times in Recent changes, page histories, and contribution histories based on your local time zone. However, when you sign a talk page with ~~~~, the timestamp is created in text, so it has to be displayed in UTC. Automated logs such as image file uploads are also shown in server time (UTC).

To show other users what time zone you are in, you could even add a time userbox to your own user page.