When the sun's and moon's gravity pull on the earth, they cause tides.
For instance, the moon pulls the water towards it, causing the ocean on the near side of the earth to bulge out in the moon's direction. At the same time, the moon pulls the earth away from the water on the opposite side of the planet, causing a corresponding bulge of water on that side. There are two high tides and two low tides every day, separated by about 12 hours and 25 minutes. This happens because the earth rotates 180 degrees in 12 hours, while the moon rotates 6 degrees around the earth in 12 hours. Even if the moon escaped its orbit, there would still be solar tides on earth, but the daily low and high tides would be much smaller.
There are several different types of tides. Neap tides are especially weak tides that occur during the moon's quarter phase. When this happens, the sun's and moon's respective pulls cancel each other out, so there isn't as much difference between high and low tides. Spring tides occur during the full moon and the new moon. They are especially strong high tides because the earth, the sun and the moon are aligned, so the sun and moon pull together against the earth.
The proxigean spring tide is a very high tide that only occurs when the moon is unusually close to the earth and in the new moon phase -- at most, it occurs about once every 1.5 years. Over the last 400 years, there have been 39 instances of an "extreme proxigean spring tide" -- the most severe form. The last occurred on March 7, 1995 during a full moon, causing tidal flooding. The next one is predicted for the year 2026.