The O2 sensor located inside the exhaust is used to detect the emissions from the engine. The O2 sensors are fitted to enable the ECU to weaken the fuel mixture to comply with the emission standards
and in certain throttle positions (mainly mid-range) will try to lean the mixture too much.
This is good for the emissions but not for the performance and smoothness of the engine.
With the elimination of the sensor:
Improve throttle response, with smoother power delivery and more torque available
Support Fuel Injection modifications like Power Commander or V&H Fuelpak
and other mods that require the elimination of the sensor.
Or you might simply want to disable a faulty o2 sensor.