For an electrical switch or relay, this means that when switch is operated, the new connection is made before the old is broken, so the center contact is momentarily connected to both contacts.
A switch with this property is useful when you never want an open circuit, for example when used as a by-pass switch.
Below is a little illustration that shows that the center contact is always connected to at least one other contact.
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0----- |0----- |0-----
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---0| => ---0| => ---0|
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|0----- |0----- 0-----
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The term is also used to describe a property of some mobile networks. Then it means that when switching networks, the new connection is established before the old is disconnected. This ensures that the link is not lost if the new connection fails.
The opposite is break before make.