A toilet wax ring can malfunction and break, leading to problems with the toilet leaking onto the bathroom floor. Some people might believe that a broken wax ring also has something to do with the toilet not flushing.
However, the wax ring really does not have much to do with the flushing mechanism of the toilet; it is there just to seal up the toilet. The toilet should still be able to flush even if the wax ring is completely broken. If you flush and the toilet water comes out from the base of the floor, your wax ring is broken.