Also known as the “Moho”. It is the boundary between the crust and the mantle of the Earth. It is found at a depth of 3-7 km beneath the ocean floor, and 25-100 km beneath continents*.
The discontinuity was discovered in 1909 by Andrija Mohorovičić, a Croatian geologist/meteorologist. He discovered the discontinuity by analysing seismograph records of earthquakes. He noticed that longitudinal p waves that travelled deeper in the Earth moved more quickly than those that travelled nearer the surface. He realized that this indicated that the interior of the Earth had a different composition to the surface. The boundary between these two types of material was named after him.
The Mohorovicic discontinuity was one of the first features of the internal structure of the Earth to be identified. This discovery and others following it led to the formulation of the continental drift and plate tectonics theories.
*
My sources vary quite widely on this point.
Sources:
http://www.istrians.com/istria/illustri/mohorovicic/
http://www.glossary.oilfield.slb.com/Display.cfm?Term=Mohorovicic%20discontinuity
http://www.informationsphere.com/html/1681.htm
http://www7.nationalacademies.org/archives/amsoc.html