In open loop the ecm measures some sensors on the engine, calculates how much fuel to inject, and does it. However, it never checks to see how well it really worked.
In closed loop it does all that but also checks a sensor (the O2 sensor) to tell it how close the calculated amount of fuel was to how much the engine really needed, and it uses that error as part of the next fuel calculation to hopefully get a better, more accurate answer. In control theory jargon this is "closing the loop" because data is fed back from the output to the input in a loop or circle.
Not to further confuse you, but I'm guessing this question came up because with a scan tool there is a "closed loop" flag that you can see. This is set once the ecm has decided, based on engine temp, O2 sensor activity, run time, and other stuff, that it is okay to start believing all the sensors and to go closed loop. However, just because all these conditions are satisfied and the closed loop flag is set, there are other reasons the ecm may not actually be in closed loop mode, usually because of recent changes in the gas pedal (acceleration, decel, or power enrichment from mashing down roughly past 1/3 throttle and holding it). So if that flag is set the ecm may be in closed loop, but if it is not set it definitely is in open loop. There is another flag, the learn flag, which tells you that the ecm is remembering the corrections so that the next time it is in open loop mode it will be closer to correct. Whenever this flag is set you can be sure that the ecm is in closed loop mode, but again there will be times when this flag is not set and the closed loop flag is set and the ecm is in closed loop mode. Hope this helped some.