Local time, or Apparent Solar Time, is the time you would read off a sun dial (if the sun were out). When the shadow on the sun dial is shortest and points straight north (in the Northern Hemisphere), it is local noon. Local noon varies by 4 minutes for each degree of longitudinal separation between two locations.
Time zones were created in the 1880s, because with the advent of train travel, people found that they had to adjust their watches to local time each time they got off the train. This was very annoying, plus sometimes people missed their appointments because of confusion over what time it was.
Time Zones are longitudinal slices of the Earth in which everyone agrees what time it is. The clock time within a time zone is called Standard Time. Standard Time can be shifted by an hour when Daylight Savings Time (US) or Summer Time (Europe) is invoked. Each longitudinal slice is approximately 15 degrees of separation.
Realizing that there was a tolerably small difference between local noons within a region of about 15 degrees longitudinal separation, western industrial countries got together and separated the world into time zones. Click on the map above to see these time zones.
One thing you'll notice from the map is that many countries have distorted the time zone boundaries for political or other reasons. For example, China spans 75 longitudinal degrees (five longitudinal slices), but insists that all of its country be within one time zone. Notice also the crooked path of the International Date Line.
One consequence of time zones is that at clock noon (12 noon, Standard Time), the Sun will be west of the local meridian for places on the eastern boundary of the time zone, and vice-versa.
The United States and its possessions span quite a few time zones. Use this applet to find out what time it is in each part of the US and its possessions (you may be surprised).
Sometimes people like to compare their local standard time to the time occurring for people living on the Prime Meridian, the longitudinal line of zero degrees that goes through Greenwich, England. The standard time for folks living on the Prime Meridian is Greenwich Mean Time, or more politically correctly, Universal Time (UT). The United States military refers to UT as Zulu Time. All three terms are equivalent.