Sidereal time is a way of measuring time based on position relative to stars, rather than relative to the sun. Measuring time by the Sun
is slightly problematic. Because we rotate around the sun, as well as on our axis, each solar day
is slightly shorter than one rotational day (about 4 minutes shore, as a matter of fact, which amounts to 1/4 day a year, hence leap year
every 4 years).
Think of it like this: if the earth were spinning around the sun, with out rotating on it's axis, all sides of earth would eventually point to the sun, because of the direction of things, it means that the earth rotates 364 rotation in 365 days. This is a problem for astronomers and their ilk, so they came up with sidereal time. Because it is relative to an object witch is stationary (for all practical purposes, the 2 AU jitter of the earth notwithstanding). In addition, sidereal time does not have time zones, so if you drove 1/48th along the equator, the sidereal time would be 1/2 hour different from where you were.
There are numerous sidereal time calculators on the internet, try http://www.jgiesen.de/astro/astroJS/siderealClock/.