whats the IAC valve?

this o2 sensor suggestion keeps on coming up... for me at least. bad gas mileage and my car, d16z6 auto, idles sometimes extremely low (400rpm) so the car is shakin... sometimes i'll start it and it'll immediately stall out cuz it'll start to idle too low... hopefully i'm makin sense.

when you're idling, is the 02 sensor controlling the a/f mixture? I never got a definiate answer when its closed loop and when its open loop... so my mileage is compromised...