A fxBreakGeometry node is generated when a user selects one or more mesh nodes and from the Fracture menu clicks: Fracture > Break selected. A fxBreakGeometry is created for each mesh node. The fxBreakGeometry node is created with a child particle node.
The particle node is what represents the point cloud that is used by the voronoi algorithm to generate the fragments. Voronoi is the default fragment option. Though accessible in the basic Maya Attribute Editor the attributes are also, and is recommended, cab be accessed from the Break properties panel found in the Inputs tab.