lambda (oxygen) sensor
your engine management (ecu) needs information from the lambda sensor on how well the engine is burning fuel by measuring the amount of oxygen in the exhaust. this in turn tells the ecu by how much more or less to fuel, also based on a lot more information got from other sensors: air temp, coolant temp, manifold pressure etc. all this happens.. before you've had time to cough
so yes, you really do need the o2 sensor, in good and proper working form. get a pic up of how badly damaged yours is. we may be able to advice on whether to leave it as-is or replace.
here's a much much muuuuuuuuuuch
more detailed explanation from wiki..