A day is the time it takes Earth to spin once around on its axis relative to some external reference. The two main references are the Sun, which leads to the solar day, and the stars, which leads to the sidereal day.
The apparent solar day is the interval between two consecutive upper culminations (or upper transits) of the Sun, i.e., the period between one passage of the Sun at maximum altitude across the observer's meridian and the next. The apparent solar day varies with the time of year because the Sun moves in the ecliptic instead of along the celestial equator, and also because the Sun moves along the ecliptic at a variable rate (due to the varying distance of Earth from Sun during the year). The mean solar day is the average of the apparent solar day over a whole year or – what amounts to the same thing – the length of day reckoned according to the mean sun.
The equinoctial sidereal day is the interval between two successive meridian transits of the vernal equinox (equal to 23h 56m 4.091s). Because of precession, the sidereal day is about 0.0084 second shorter the true sidereal day, which is the period of Earth's rotation relative to a fixed direction, i.e., the interval between two successive upper transits of a star from a fixed point on Earth's surface.