O2 Sensor Discusion / Programmer

[mwm13]

I thought the reason for O2 sensors being there was to maximize the most efficient way your engine would run by reading the exhaust gases and then adjusting air fuel mixture, in turn raising your mileage and performance? If you just bypass it or cut it out wouldnt your engine run less efficient? Im probably wrong Ive just always thought thats why O2 sensors were there, Im currently getting a check engine light right now reguarding my O2 sensors, and I get 13MPG combined out of my 1998 GMC sierra with 350 vortec currently stock with 3.73's ive been planning on replacing my sensors assuming my mileage would go up but if they dont do anything along those lines I wont bother. If i buy a programmer or get a tune does this mean I will no longer need my O2's? If someone could explain the true purpose of these thing that would be awesome thanks alot!