If there was no moon then the Earth's tilt would could vary wildly which means that without the moon, the earth would move from no tilt to a large tilt.
With no tilt of the earth the earth would have no seasons.
When the earth has a large tilt there would be extreme weather and ice ages.
Without the moon, the axial tilt of the earth would become unstable and result in unpredictable and even potentially extreme seasons.
Also without the moon, tides would be reduced to around a third of their current size and the length of a day on earth would shrink down to 6 to 8 hours.
The gravitational pull of the moon, stabilizes earth's 23.5 degree axial tilt which is what is responsible for the seasons on earth.
The Moon is also the primary driver of the Earth's tides and the Sun contributes a smaller amount of tides.
Without the Moon, tides would be much smaller and only around a third of their current size.
The gravitational pull of Earth also slows the rotation of Earth and increases the length of a day by a couple of milliseconds per century.
And without the Moon, earth would also spin faster and the days would be shorter.
The Moon is also required for lunar and solar eclipses.
The Moon also provides Earth with a great amount of light at night and without the Moon the nights would be even darker.
Any changes in tides, days as well as the environment without the moon could affect evolution of life on Earth.
And many animals also rely on the lunar cycle for migration, navigation and reproductive timing.
Also the absence of the moon's reflection would also result in the sky being much darker and could reveal more stars and constellations.