For solar eclipses, Maximum is the moment when the area of the Sun's disk that is covered by the Moon is greatest, as seen from the perspective of the selected location. After that moment, the Moon starts to move away from the Sun again.
Our calculations of the maximum point of a solar eclipse at a specific location only account for the time span when the entire Sun is visible above the horizon there. If the Sun sets as the covered portion of the Sun increases, or if it rises as the covered portion decreases, the eclipse may reach a slightly greater magnitude during the time when only part of the Sun's disk is visible.
For lunar eclipses, Maximum is the moment when the Moon is closest to the center of Earth's shadow. For locations where the Moon is below the horizon at that moment, Local max is shown in addition. This is the instant when the eclipse reaches its greatest magnitude while the entire Moon is above the horizon in the selected location.
The local max usually occurs either just after moonrise or just before moonset. Please note that moonrise and moonset times assume a flat horizon, which is at the same altitude as the observer. This means that the Moon may not be visible at the moment of local max if there are obstacles in the way, such as hills, buildings, or clouds.