No, each day is not exactly 23 hours, 56 minutes, and 4 seconds long. That particular duration corresponds to what is known as a sidereal day, which is the time it takes for the Earth to complete one rotation relative to the distant stars. However, due to various factors, including the Earth's orbit around the Sun and its axial tilt, we use a different measure of time known as the solar day for our everyday lives.
The solar day is the period of time from one noon to the next, as indicated by the position of the Sun in the sky. It is slightly longer than the sidereal day, lasting approximately 24 hours on average. This discrepancy occurs because, during the time it takes for the Earth to complete one rotation, it has also moved a little along its orbit around the Sun.
To account for this difference, we introduce leap seconds periodically to our timekeeping systems. Leap seconds are added or subtracted to keep our clocks in sync with the Earth's rotation, ensuring that noon remains relatively close to when the Sun is at its highest point in the sky.
Therefore, while a sidereal day is approximately 23 hours, 56 minutes, and 4 seconds long, the solar day, which is the basis of our 24-hour day, averages out to around 24 hours with the introduction of leap seconds to align our timekeeping with the Earth's rotation and the position of the Sun.