Zero thickness geometry is when a feature is created that can not be solved due to the fact that there is precisely zero material at only a point or an edge. An example would be if you created an extruded circle that is tangent to an extruded square. There is a good explanation here: http://help.solidworks.com/2012/English/SolidWorks/sldworks/HIDE_ZeroThickness.htm
I've reposted the general guidelines from that site below as reference.
Every edge of a solid body must have exactly two adjacent faces.
Edge where zero thickness geometry is located.
Vertices where zero thickness is located.
Tangent line where zero thickness is located.
Zero thickness occurs when you attempt to extrude a cut tangent to a hole.
This is frequently the cause of failed section views in drawings.