For an electrical switch or relay, this means that when switch is operated, the old connection is broken before the new is made, so the center contact is momentarily disconnected from both contacts.

A switch with this property is useful when you never want to short circuit the other contacts.

Below is a little illustration that shows that the center contact is never connected to more than one other contact.

     0-----            0-----           |0-----
                      |                 |
---0|         =>  ---0|         =>  ---0|
    |                 |        
    |                 |        
    |0-----            0-----            0-----

The opposite is make before break.