Sidereal Day Versus Solar Day
As Earth rotates, the sun and stars appear to move in relation to it. The solar day derives from Earth's rotation with respect to the sun, which causes the phenomena of "sunrise" and "sunset." "Noon" is the halfway point in a solar day, when the sun is at its highest point in the sky. By contrast, the sidereal day measures Earth's rotation with respect to background stars. Because these stars are much farther away, Earth's position with respect to them changes only to a miniscule degree.
Sidereal Time Difference
In general, sidereal time and solar time are fairly similar: One sidereal day lasts about 23 hours, 56 minutes and 4.1 seconds, which is roughly four minutes shorter than the solar day. Over the course of a year, however, this adds up to one full day. This relationship isn't coincidental, and helps to demonstrate how solar and sidereal days differ.
Why a Difference Exists Between Solar and Sidereal Days
As Earth spins on its polar axis, it also moves around the sun, taking about 365 days to complete a full orbit. In 24 hours, Earth completes one rotation (causing the sun to "move" in the sky), and it also completes 1/365th of its orbit around the sun. Because of this change in orbital position, Earth has to turn for an additional 4 minutes (i.e., 24 divided by 365) in order for the sun to appear to be in the same place as it was on the previous day. Earth's motion with respect to distant stars is much smaller, so the sidereal day does not need to take this orbital difference into account.
Effects of Sidereal Time
Even if you've never heard of sidereal time, you're probably intuitively familiar with its effects. If you've ever stargazed, you know that some constellations are "summer" constellations and others are "winter" constellations, depending on where you live. The difference between solar and sidereal time is responsible; eventually, the gap between the sidereal day and the solar day reaches the point where stars that would normally be hidden by the sun are visible at night.