The Hawaiian Islands are in the next to the last time zone, which is Universal Time (UT), also called Greenwich Mean Time (GMT), minus 10 hours. This places Hawai`i two hours east of the International Dateline.
Hawaii Standard Time (HST) does not adjust for Daylight Savings, keeping the same time year-round. This means that the islands are three hours behind the west coast of the U.S. in summer, two hours in winter, and are six hours behind the east coast in summer, five hours in winter.
The phrase "Hawaiian Time" refers to the laid back pace that one finds in the islands. For newcomers, it can seem like it takes longer for things to get done, and this may be true. Longer term residents know it has more to do with allowing time for all that is important, taking things as they come, or perhaps "going with the flow" is most descriptive.
You can find a long list of "time-ly" words and phrases, such as minute, second, hours, days of the week, months of the year and much more at The Hawaiian Language Site: Ka Manawa (time).