What is the difference between a proportional thermostat and an on/off thermostat?

An off/off style thermostat turns the heater on full power when the temperature gets too low.  Then it turns it completely off when the temperature gets too high.  This style create a wider swing in temperature because the temperature has to get too high or low before the thermostat responds.  The proportional style thermostat adjusts the power up and down as the temperature starts getting close to the set-point (your target temperature).  It will reduce the amount of power going to the heater as the temperature gets close to the set-point.  Then it will increase the power as the temperature starts falling away from the set-point.  This allows the temperature swing to be much less than the on/off style thermostat.  When incubating eggs, accuracy counts!  That is why a proportional style thermostat is preferred.