Answer:
Very generally, a closed-loop system will have some form of feedback that regulates the system behavior, whereas an open-loop system does not have this feedback.
As a simple example, imagine you driving a car on a freeway: your car enters at 50 MPH and you want to be driving at 65 MPH. You know that if you depress the pedal at a certain degree for a certain amount of time, you will eventually accelerate the car to 65 MPH. In an open-loop system, you would have to make the best guess for the angle and amount of time you need to depress the pedal. In a closed-loop system, you are watching your odometer in order to see that you've actually increased your speed to 67 MPH and need to lay off the gas a bit.
More importantly, if your car encounters a hill your closed-loop system will be able to recognize the fact that you require more acceleration to maintain your speed, whereas your open-loop system might slow down a lot.
It should be clear from this example that closed-loop systems are in general more robust to changes in the system state that aren't considered in your model.