The gravitational force that holds the earth and the moon together is generated from a common center of mass located in the earth. But because this point is different from the center of the earth, it causes a slight wobble in the earth-moon system. The centrifugal force caused by this motion causes the water on the surface of the earth to bulge out on the side that is furthest from the moon. On the side closest to the moon, the gravitational pull from the moon itself is strong enough to counteract this centrifugal force, and so the water on this surface of the earth bulges out as well. Water underneath either of these bulges would naturally be deeper than the water that was located away from them, and as the earth spins on its axis, a point on the planet's surface will go from being underneath a bulge to not being underneath a bulge, respectively causing high and low tides.
But the moon is not the only body in the solar system that has an effect on the tides. The sun also has the same effect on the tidal bulges as the moon, and when the sun and the moon are in line with one another as they are during a new moon and a full moon (like the one that occurred just a few days ago), the effects combine to create even higher tidal ranges. This rise and fall in sea level is a twice-daily reminder of how connected we are to things outside of our world. Tide goes in, tide goes out. Never a miscommunication. You can't explain that. Oh, wait, I think I just did.