ZIF - Zero Insertion Force Connectors
ZIF is an acronym for Zero Insertion Force, it's a socketing method for providing non-soldering circuit connections on PCBs, while ZIF covers things like CPU sockets this article specifically discusses ZIF in relationship to 1.8" hard drives which are found in portable electronics such as the iPod or embedded systems. Similar to ZIF are LIF sockets, LIF is an acronym for 'Light Insertion Force'.
Most HD ZIF connectors have a locking mechanism that might not be apparent if you are unfamiliar with them, I've attached an animated gif that shows how the mechanism works. If you are attempting to remove a ZIF connector you must disengage the locking mechanism before you remove the ZIF cable, failure to do so can scrap the contact material off the cable rendering it useless. As well make sure you engage the locking mechanism after insertion to ensure that the cable doesn't jostle out or misalign.
Figure 1. - ZIF Cable Locking Mechanism - Pull-out Style
Another important aspect of the ZIF connector is the number of 'matings' that can be performed before the socket becomes unreliable. Most manufactures rate their maximum mating limit as 30, so keep that in mind as you work with a ZIF socket, you don't have the forgiveness that SATA or IDE provide in terms of socket mating. Comparatively LIF sockets have only a recommended 10 mating maximum.
One final note, the 'Zero' isn't a joke in the acronym, do not force the cable, verify that it is aligned correctly as misalignment can send voltage places it's not supposed to go.