Sidereal time literally means 'star time'. The time we are used to seeing in our every day lives is mean 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.
However, there is a problem with solar time. The earth does not actually spin 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 travelled 360 degrees around the sky
Astronomers are concerned with how long it takes the earth to spin in respect to the fixed stars, not the sun. An astronomer needs a timescale that removes the complication of the earth's orbit around the sun, and 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 one 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.