Cool question! We sometimes forget about what that big rock in the sky does for the earth, but it is incredibly important.

The short answer (and most important thing): The moon has stabilized life on Earth. If the moon did not exist, life on Earth would most likely be totally different.

Long answer: The most accepted theory on how the moon got here was that a large rock smashed into the earth (about 10% the size of our planet) when it was still in its molten stage (~95 millions year ago). This knocked off a large part of the earth which is the moon. Why do they say this? The elemental composition on the moon and Earth are incredibly similar, which is too unlikely to be a coincidence.

The moon has a large impact on our tides, which is due to the gravitational pull of the moon. As the moon circles the earth, the moons gravity pulls on bodies of water that are closest to the moon, causing high tides there, which makes those a quarter away around the earth become low. Due to the Inertia effect of water, tides on the other side of the earth also rise. If there was no moon, the tides would not be this predictable.

Finally, due the moon stabilizing some of the "wobble" of the earth's spin (which also ends up slowing the spin of the earth down just a little bit, which also makes the earth tilt consistently a certain way), the moon has stabilized the seasons on earth. Over billions of years, this kind of effect is thought to have enabled life on earth to develop the way it has. If we didn't have the moon, who is to say what life on earth would look like...?

Here is a great video showing the simulation of our moon formation:

watch