closed loop is when the ECU uses the results from the oxygen sensors in the exhaust to modify the air/fuel ratio to maintain the desired 14.7:1 ratio requried for the cats to work correctly.
open loop is when the oxygen sensors aren't used and the air/fuel ratio is based purely on input sensors (air temp, throttle position, air flow, engine temp etc.) and a preprogrammed map held within the ECU. As there is nothing checking the output the ECU has no way of knowing if the fuelling is actually correct.
open loop is used when the 14.7:1 ratio is not required. For example when the engine is cold or when it is hard accelerating, both of these require a richer mixture.