It is a cylinder that lets you open from outside with your key even if another key has been left in on the inside.
With a standard cylinder, if someone leaves the key in on the inside, the key from outside will not go in or will not turn. It happens a lot in homes with children or elderly people, or when someone locks up at bedtime and leaves the key in. The result is that whoever arrives is stuck outside, or nobody can get in to help the person inside.
The double clutch, also called an emergency function, solves exactly that. It is a feature you can ask for on security cylinders, so you do not have to choose between one thing and the other.
If people in your house often leave the key in on the inside, it is one of the most useful upgrades. More in cylinder replacement.