The word "sidereal" means "relating to the stars". It derives from the Latin sidus, meaning "star".
As the Earth orbits the Sun, the apparent position of the Sun against the stars gradually moves along the ecliptic, passing through the twelve traditional constellations of the zodiac, and returning to its starting point after one sidereal year. This motion is difficult to observe directly because the stars cannot be seen when the Sun is in the sky. However, if one looks regularly at the sky before dawn, the annual motion is very noticeable: the last stars seen to rise are not always the same, and within a week or two an upward shift can be noted. As an example, in July in the Northern Hemisphere, Orion cannot be seen in the dawn sky, but in August it becomes visible.
This effect is easier to measure than the north/south movement of the position of sunrise(except high latitude region), which defines the seasonal cycle and the tropical year on which the Gregorian calendar is based. For this reason many cultures started their year on the first day a particular special star (Sirius, for instance) could be seen in the east at dawn. In Hesiod's Works and Days, the times of the year for sowing, harvest, and so on are given by reference to the first visibility of stars. Such a calendar is effectively using the sidereal year.
Up to the time of Hipparchus, the years measured by the stars (sidereal years) were thought to be exactly as long as the years measured by the seasons (tropical years). In fact, sidereal years are very slightly longer than tropical years: one sidereal year is roughly equal to 1 + 1/26000 or 1.000039 tropical years. The difference is caused by the precession of the equinoxes, and means that over long periods of time a calendar based on the sidereal year will drift out of sync with the seasons at the rate of approximately one day per 71.6 years.
Early astronomy books such as “A Short History of Astronomy” by Arthur Berry (published 1899) state that “a sidereal year describes an arc of 360 degrees” whereas the tropical year represents an arc reduced by 50 arc seconds or “359 degrees, 59 minutes and 10 arc seconds”. This description is correct when measuring the motion of the earth relative to the stars and is still the most common method used today.
However, when measuring the motion of the earth relative to the sun (via earth rotation studies or lunar rotation studies) astronomers find the tropical year describes an arc of 360 degrees and the sidereal year is 360 degrees and 50 arc seconds. Again the difference is due to precession, however the reason for the different measurements is the first uses a static solar system model (non moving solar system) and the later uses a dynamic solar system model (a moving solar system).