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An apparent sidereal day is the time it takes for the Earth to turn 360 degrees in its rotation; more precisely, is the time it takes a typical star to make two successive upper meridian transits. This is slightly shorter than a solar day. There are 366.2422 sidereal days in a tropical year, but 365.2422 solar days, resulting in a sidereal day of 86,164.09 seconds (or: 23 hours, 56 minutes, 4.09 seconds).
The reason there is one more sidereal day than "normal" days in a year is that the Earth's orbit around the Sun cancels one sidereal day out, giving observers on Earth 365 (and a quarter) days, even though the planet itself rotated 366 (and a quarter) times (the Earth rotates in the same direction around its axis as it does around the Sun: seen from the northern sky anti-clockwise).
Midnight, in sidereal time, is when the First Point of AriesThe First Point of Aries also called the vernal equinox point is one of the two points on the celestial sphere where the celestial equator intersects the ecliptic. It is defined as the position of the Sun on the celestial sphere at the time of the vernal crosses the upper meridian.A mean sidereal day is reckoned, not from the actual transit, but from the transit of the mean vernal equinox (see: mean sun).