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Time measurement is based on mostly regular natural phenomena, such as alternating light and dark periods caused by the rotation of the planet. The total time taken by two successive periods is constant, but the lengths of the light and dark period vary. One simple constant is noon.
Noon is the time of the day when the Sun is at its highest position. Since (according to recent research) the Earth is round, noon happens at different times in different places. This leads to the concept of local time. Humans measure time in many units, most of which are tied to natural phenomena like noon. As long as you stay in the same place, it doesn't matter that local times differ.
As soon as you need to communicate with distant places, you'll notice the need for a common time. In modern times, most of the places in the world communicate with most other places in the world, so a global standard for measuring time has been defined. This time is called universal time (UT or UTC, formerly known as Greenwich Mean Time or GMT, since it used to be local time in Greenwich, England). When people with different local times need to communicate, they can express times in universal time, so that there is no confusion about when things should happen.
Each local time is called a time zone. While geography would allow all places that have noon at the same time have the same time zone, politics makes it difficult. For various reasons, many countries use daylight savings time, that is, they move their clocks to have more natural light while they work, and then move the clocks back during winter. Other countries do not do this. Those that do, do not agree when the clocks should be moved, and they change the rules from year to year. This makes time zone conversions definitely non-trivial.
Time zones are best named by the location or by telling the difference between local and universal time. In the US and some other countries, the local time zones have a name and a three letter abbreviation. The abbreviations are not unique, however, and should not be used unless the country is also named. It is better to talk about the local time in, say, Helsinki, than about East European time, since not all countries in Eastern Europe follow the same rules.
Linux has a time zone package that knows about all existing time zones, and that can easily be updated when the rules change. All the system administrator needs to do is to select the appropriate time zone. Also, each user can set his own time zone; this is important since many people work with computers in different countries over the Internet. When the rules for daylight savings time change in your local time zone, make sure you'll upgrade at least that part of your Linux system. Other than setting the system time zone and upgrading the time zone data files, there is little need to bother about time.