Moon is not indispensable for existence of life on Earth. However its absence can surely alter the way the Earth functions. Moon’s gravitational pull is responsible for high tides and low tides. If there was no moon there wouldn’t have been any high tides and low tides. But tides still would have occurred because sun too has gravitational pull which can cause them.
Gravitational pull of the moon causes the earth to rotate a little slowly than it would have in its absence. So if the moon disappeared, the earth will rotate faster. This will make the day time a little shorter than it is.