If you look at the Calendar API JavaDoc for these constants, it explains that these values are used as values for the 'field' parameter for the Calendar's set(int field, int value) and get(int field) methods. For example, in the following code, I use the Calendar.ZONE_OFFSET to determine the Greenwich Mean Time (GMT) offset for my computer.
Note that the TimeUnit Enum I use was added in Java 5, and the HOURS was added to that Enum in Java 6. For older versions of Java, you can just do the math yourself.
So basically, these values (along with others in the Calendar class) tell the get and set method what field of the calendar you want the operation to occur on.
In the case of the the GMT offset, I could have done this in a different way:
[ November 11, 2008: Message edited by: Mark Vedder ]