UTC stands for Coordinated Universal Time, and for this purpose is the same as GMT (Greenwich Mean Time).
Since the USGS and other seismic network agencies record earthquakes around the globe in all the various time zones, using a single standard time reference is best for record-keeping and exchange of data. The individual event pages with details about each earthquake use UTC for the reference time. Sometimes this means the UTC date of the earthquake is "the next day" from the date where you are.
The default time reference on the Latest Earthquakes list is your local time based on the time clock on your computer or mobile device. You can change this setting in the Settings panel ("gear" icon in upper right). Keep in mind that your local time might be different from the local time of the earthquake, even if you felt it. An earthquake offshore in the ocean or in a neighboring state might be in different time zone from yours.
NASA has a helpful website on Time Zones and Universal Time.