Sidereal Time literally means “star time”. The time we are used to using in our everyday lives is Solar Time. The fundamental unit of Solar Time is a Day: the time it takes the Sun to travel 360 degrees around the sky, due to the rotation of the Earth. Smaller units of Solar Time are just divisions of a Day:
1/24 Day = 1 Hour
1/60 Hour = 1 Minute
1/60 Minute = 1 Second
However, there is a problem with Solar Time. The Earth does not actually spin around 360 degrees in one Solar Day. The Earth is in orbit around the Sun, and over the course of one day, it moves about one Degree along its orbit (360 degrees/365.25 Days for a full orbit = about one Degree per Day). So, in 24 hours, the direction toward the Sun changes by about a Degree. Therefore, the Earth has to spin 361 degrees to make the Sun look like it has traveled 360 degrees around the Sky.
In astronomy, we are concerned with how long it takes the Earth to spin with respect to the “fixed” stars, not the Sun. So, we would like a timescale that removes the complication of Earth's orbit around the Sun, and just focuses on how long it takes the Earth to spin 360 degrees with respect to the stars. This rotational period is called a Sidereal Day. On average, it is 4 minutes shorter than a Solar Day, because of the extra 1 degree the Earth spins in a Solar Day. Rather than defining a Sidereal Day to be 23 hours, 56 minutes, we define Sidereal Hours, Minutes and Seconds that are the same fraction of a Day as their Solar counterparts. Therefore, one Solar Second = 1.00278 Sidereal Seconds.
The Sidereal Time is useful for determining where the stars are at any given time. Sidereal Time divides one full spin of the Earth into 24 Sidereal Hours; similarly, the map of the sky is divided into 24 Hours of Right Ascension. This is no coincidence; Local Sidereal Time (LST) indicates the Right Ascension on the sky that is currently crossing the Local Meridian. So, if a star has a Right Ascension of 05h 32m 24s, it will be on your meridian at LST=05:32:24. More generally, the difference between an object's RA and the Local Sidereal Time tells you how far from the Meridian the object is. For example, the same object at LST=06:32:24 (one Sidereal Hour later), will be one Hour of Right Ascension west of your meridian, which is 15 degrees. This angular distance from the meridian is called the object's Hour Angle.
The Local Sidereal Time is displayed by KStars in the Time Info Box, with the label “ST” (you have to “unshade” the box by double-clicking it in order to see the sidereal time). Note that the changing sidereal seconds are not synchronized with the changing Local Time and Universal Time seconds. In fact, if you watch the clocks for a while, you will notice that the Sidereal seconds really are slightly shorter than the LT and UT seconds.
Point to the Zenith (press Z or select the → menu item). The Zenith is the point on the sky where you are looking “straight up” from the ground, and it is a point on your Local Meridian. Note the Right Ascension of the Zenith: it is exactly the same as your Local Sidereal Time.