The solar day is the day measured relative to the Sun's position iin the sky: when the Sun reaches the same longitude in the sky, one solar day has passed. This actually means that the Earth has rotated once with respect to the Sun, but the Earth is also moving around the Sun, so the time taken for the Earth to rotate in space (relative to the fixed stars) is not the same as the solar day. We set our clocks according to the solar day.
The sidereal day is the time taken for the Earth to rotate once on its axis relative to the fixed stars. While the Earth is rotating on its axis it is also moving along its orbit around the Sun. Over the course of a day the Earth moves almost one degree of arc around the Sun (360/365 of a degree).
The Earth rotates about 360/24=15 degrees in one hour, so one degree of rotation is equivalent to about four minutes of time. A star that rises at 10:00pm tonight will rise at 9:56 pm tomorrow and at 9:52pm the following night, and will also set four and eight minutes earlier respectively. One month later that star will rise or set two hours earlier. In other words, from our perspective, the stars revolve around the Earth in only 23 hours and 56 minutes. This period is known as a sidereal day.
