I hear a lot of people refer to Zif sockets incorrectly like a name brand or a specific connector. Like injungleist said it stands for Zero Insertion Force, and technically it could cover an wide variety of connectors including a FFC/FPC connector.
In this case it would be a Zif FPC connector. One that many people are familiar with are dip zif sockets. they are the green ones with a little lever that can handle dip chips that you find on some programmers.
Zif is like a descriptor the same way a "keyed" connector or a "locking" connector would be used, but be careful as it is terminology that may or may not be used by the manufacturer to describe that kind of connector. there are low insertion force connectors as well.