During a full moon, the moon is essentially lined up on the opposite side of the Earth from the sun and the gravitational tug of war between those two intensifies, resulting in higher tides.

5:59PM EDT October 29. 2012 - Higher-than-normal tides -- tied to a full moon -- have added to Hurricane Sandy's coastal flooding threat.
As you might expect the explanation is a matter of simple astronomy, not any kind of lunacy associated in folklore with a full moon.
"It's not the moon's phase that matters, but the position," says astronomer Phil Plait on his Bad Astronomy website.
During a full moon, the moon is essentially lined up on the opposite side of the Earth from the sun (this is what allows the near surface of the moon to be illuminated in its full splendor) and the gravitational tug of war between those two intensifies at this time, resulting in higher tides.
This kind of alignment of astronomical objects is called a syzygy (SIH-zhih-jhee) and sailors have understood the effect for centuries. So, for Hurricane Sandy, the higher-than-normal tides that threaten to add to an 11-foot storm surge feared for lower Manhattan are simply a matter of bad timing.
When a full moon comes during the time when the moon is at the lowest point of its slightly-out-of-round orbit, the result is a supermoon", as NASA calls it, when the full moon looks a bit bigger in the nighttime sky because it is a tad closer to Earth.
The moon's gravity triggers about two-thirds of a typical tide's size and the sun is responsible for another third, so when they line up, higher tides almost always result. A similar alignment and similar higher tides happen during a new moon, when the moon aligns between the Earth and sun.
http://www.usatoday.com/story/tech/sciencefair/2012/10/29/sandy-full-moon-tide/1666479/