The moon is very important to earth and there would be a list of things that would happen.

The gravitational pull that exists between the moon and the earth is responsible for the tides. if we take that away we will have a total imbalance that could be catastrophic. Sea life would be disrupted as currents and tides help sea life exist.

The earth would spin a little faster without the moon changing the length of days making them shorter. This would put our calendars and clocks out of sync.

Scientists believe that Earth's current tilt is a byproduct of the huge collision that produced the moon millions of years ago, and is only held stable by its continued orbiting around earth. So, without a moon, the Earth’s axis could dangerously shift. This could lead to large portions of Earth becoming uninhabitable.