The astronomer Richard Nolle coined the term "Super Moon" which means a new or full moon at 90% or greater of its closest perigee to Earth. Well on March 19th the moon will be at perigee (its closest position in its orbit to Earth). This will be the closest perigee in 18 years.
The largest effect will be on the tide which occurs at the full moon every month as the closer to the earth the moon orbits, so the effect on tides increases. A 5% increase in proximity makes about 20% difference in the power the moon exerts so those in coastal regions should anticipate stronger tides.
An extreme "SuperMoon" is when the moon is full or new as well as at its 100% greater mean perigee (closest) distance to earth. By this definition, last month's full moon, this month's and next month's will all be extreme "SuperMoons".
Some largely internet-based claims say such events are related to catastrophies such as extreme siesmic events or extreme weather and some coincidential strong events have happened at the same time as Super Moons, however no definitive scientific research has concluded that.