Open Loop Closed Looppicture a circuit involving the ecu and o2 sensor. Closed loop (a complete circuit) allows the ecu to receive signals (a voltage) from the o2 sensor and the ecu will translate this information and correct the fueling. In open loop (an incomplete circuit) the ecu does not receive this signal (a voltage) from the o2 sensor and thus reads straight from a pre-existing map placed on the ecu from the factory.
When a tune is done in full (the 600 dollar one) I tune in open loop and leave it in open loop. This is because i can run the engine leaner than what closed loop will allow me to and thus you will get better MPG and the engine will run better. In this mode, i dont need an o2 sensor correcting the fuel in the background because it is already perfect. I simply rely on the factory coolant and intake temp fuel corrections to fix any discrepancies in fuel.
however, on the dyno, it is more difficult and time consuming to achieve this goal. So i tune to the parameters needed to keep the o2 sensor happy in closed loop for part throttle.