Priority function means that a double cylinder can be closed from the outside if a key is inserted on the inside. The outside always has priority in the operation of the cylinder.
This is not possible the other way. In practice, it actually does not happen that you leave the key inserted on the outside and still have to open or close from inside.
Inside the profile cylinder is a one-sided spring element, the so-called priority clutch. Through this, the "extra length" of the key tip of the second key (inside) is absorbed.
In contrast, there is the Emergency and danger function.