Sidereal time refers to the length of days and other measurements of time with respect to stars other than our sun. Whereas a solar day lasts 24 hours, a sidereal day is about four minutes shorter. In everyday life, solar time is always used, but astronomers often find it useful to use sidereal time when expressing the apparent movement of stars in the sky, as observed from earth. The word "sidereal" comes from the Latin word sider, meaning "star."
Because the earth orbits around the sun as it rotates, the earth must rotate slightly more than one full rotation on its axis to complete one solar day. In one day, the earth moves through a small portion of its orbit around the sun, slightly changing the apparent angle at which the sun faces the earth. This small addition of about one degree to the angle of the sun means that the earth must rotate for an additional four minutes to "catch up" to where the sun was shining precisely one rotation ago.
However, because stars other than our sun are mostly very distant, it only takes a full rotation of 360 degrees until a distant star is back at its starting point above the earth. This rotation of 360 degrees is called a sidereal day, and it lasts 23 hours, 56 minutes, and four seconds. In a solar day, the earth rotates about 361 degrees on its axis, taking a full 24 hours.
Astronomers often use sidereal time because they are concerned with how long it takes the earth to spin, with respect to distant stars, rather than the sun. Sidereal time gives us a way to measure time that does not depend on the sun. This removes a slight mathematical complication and focuses exclusively on how long it takes the earth to rotate 360 degrees with respect to the stars.
To an astronomer, the sky is like a map, divided into 24 hours. Sidereal time helps these scientists determine where a given star or set of stars is, at any given time. The difference between solar and sidereal time is not much over an hour or a day, but adds up to a very large difference over a period of months and years. This can be observed even without a telescope. If a person were to look at or photograph the night sky at the same time every night, he would notice that the stars as a whole shift to the west over time.