This is going to be hard for me to explain but I will try my best.

The goal for the O2 sensor is not to provide the ideal fuel-air mixture for
economy or performance although that is a benifit. The 3 way catalytic
converter is so named as it is designed to reduce hydrocarbons, (HC), carbon
monoxide,(CO) and oxides of nitrogen, (NOx). The reduction of CO and HC
requires an "oxidizing" approach to both burn off the HC and add that "O"
atom to make CO become CO2. This requires excess O2 to be available or a
lean mixture. The "reduction" of the NOx requires an oxygen deficiency and
some hydrogen and carbon to reduce the NOx to water vapor and CO2.  So the
O2 system oscillates from lean to rich so that both of those reactions can
occur.

The OBDII vehicles also get feedback from sensors after the cat(s) to
further test that the cats are working. The wideband approach allows for
more sensitivity as feedback is also used after the cat(s).

http://en.wikipedia.org/wiki/Catalytic_converter

Dennis