For a few days the Moon disappears as it lies in the same direction as the Sun. This is the time of the New Moon when sunlight falls on its far side.
On rare occasions the Moon passes directly between the Earth and Sun causing a Solar Eclipse, this can only occur at a New Moon.
A Lunar Eclipse however can only occur at Full Moon, this is when the Moon passes into the shadow of the Earth.
Tides are also controlled by the Moon in conjunction with the Sun though the Moon is the dominant player in this. The relative positions of Sun, Earth and Moon, and the rotation of the Earth account for the tidal effect and the extremes of tidal range that result in Spring and Neap tides, and is shown very simply in the following diagram:
A more detailed explanation of the tidal effects is given in the following links:
and tide prediction tables are to be found on the National Tidal and Sea Level Facility.