"Beach ball" is an informal term. In technical contexts, call them focal mechanisms.
The waves from an earthquake radiate outwards, with a pattern of 4
quadrants. In two quadrants the first motion will be compressional
(a push), and in the other two extensional (a pull). The first
motion observed on a seismograph will be either up or down. Figure from Wikipedeia. 

The first motions are plotted on a sterographic projection,
differentiated by whether the ground moved up or down (the "first
motion"), and then two
orthogonal great circles are drawn to separate the up and down motions
into 4 quadrants. The quadrants are then colored, with black used for the compressional or up quadrants. For a map display of many faults, the black quadrants can be color coded by depth of the focus or the the magnitude. The two great circles represent the nodal planes for the earthquake. One will be the fault plane, and the other the auxiliary plane. There is no way from the seismic data to differentiate the two. You can get a strike and a dip for each nodal plane. These orientations will generally be consistent in a region, and reflect the state of stress in the crust. Each Fault type has a distinctive beach ball pattern, reflecting the orientations of the responsible stresses. These principal stresses are shown with the P, T, and N points, which represent lines. Figure from Wikipedeia. 
Last revision 1/6/2016