The simple answer of what happens at the boundaries of plates is that they are constantly moving and their movement defines them.  There are three different types of plate boundaries: convergent, divergent and conservative plates.  The divergent plates are constantly moving apart and magma flows up between them creating more ocean floor.  Convergent plates overlap and the magma which rises stays beneath the plates to  forms ridges.   The conservative plates don't create or destroy ocean floors but just slide back and forth. The conservative plates are the cause of earthquakes such as we see in California.