Hour

In modern usage, an hour is defined as a unit of time 60 minutes, or 3600 seconds in length. It is approximately 1/24 of a median Earth day.

Earlier definitions of the hour:

One twelfth of the time from sunrise to sunset. As a consequence, hours on summer days are longer than on winter days. Romans and Greeks used this definition and divided the night into three or four night watches. Later, the night (i. e., the time between sunset and sunrise) was also divided into twelve hours. When a clock showed these hours, its speed had to be changed every morning and evening, for example by changing the length of its pendulum.
One twenty-fourth of the apparent solar day (between one noon and the next, or between one sunset and the next). As a consequence, hours vary a little, as the length of an apparent solar day varies throughout the year. When a clock showed these hours, it had to be adjusted a few times in a month.
One twenty-fourth of the mean solar day. See mean sun for more information on the difference to the apparent solar day. When an exact clock showed these hours, it had te be adjusted virtually never. However, as earth rotation slows down, this definition has been abandoned. See UTC.

Counting hours

Every definition of the hour came with its own starting point for counting the hours.

In antiquity, the counting of hours started with sunrise. So, sunrise is always exactly at the beginning of the 1st hour, noon at the end of the 6th hour, and sunset exactly at the end of the 12th hour.
In the so-called Italian time, the first hour starts at sunset (or the end of dusk, i. e., 1/2 hour after sunset, depending on local custom). The hours are counted 1-24. So, the sun rises at Lugano in December around 14:46 and noon is around 19:23; in June, the sun rises already at 7:51 and noon is around 15:55. Sunset is always at 24:00.

This manner of counting hours has the advantage that everyone can easily read the clock to see how much time he will have to finish his daywork without artificial light. It was introduced in Italy during the 14th century and lasted until mid-18th century, in some regions until mid-19th century. It was also used in Poland and Bohemia until the 17th century.

For the modern 12-hour clock, counting the hours starts at midnight and restarts at noon. So, sunrise is around 6:00 A.M., noon always at 12:00 P.M. (except for the equation of time), and sunset around 6:00 P.M.
For the modern 24-hour clock, counting the hours starts at midnight. So, sunrise is around 6:00, noon always at 12:00 (except for the equation of time), and sunset around 18:00.

Sunrise and sunset are much more conspicuous points in day than noon or midnight; starting to count then is much easier than starting at noon or midnight. With modern astronomic equipment (and the telegraph or similar means to transfer a time sign in a split-second), this issue is no more relevant.

Sundials often show the hour length and count according to one of the older definitions and countings.

There are probably 12 hours because there are approximately 12 lunar months in a solar year. Symmetries of this sort are common in ancient units of measurement.