In horse tack, a panic snap is a mechanism often used between a lead and a horse harness or halter. They are useful because, unlike swivels or carabiners and similar fittings, they can be disconnected under load, as the panic snap is specially built so that the latching mechanism is separate from the load bearing structure.
They are sometimes dangerous, however, because leads or ropes under load can flail when freed. Panic snaps also find some use in suspension situations involving relatively light weights. Heavier masses are unsafe, with most panic snaps because of the possibility of injury from flailing cordage. They will usually require the services of a millwright.
Panic snaps are also used by motorcyclists. The snap is often connected to a braided leather strap which is connected to their left clutch lever. This type of connector allows the motorcyclist to quickly remove the snap from their leaver in the event they have to protect themselves from another motorist while riding. The snap can easily be removed with the left hand while riding and provides a very effective weapon when swung by the other end of the strap. Sometimes you will see a long leather cord hanging by the handlebars on a motorcycle, this is the concept behind this decor.
In BDSM and Bondage panic snaps are used to secure Bottoms in a safe way. They allow for a single hand to be used to release a bottom in an emergency situation. In some case the panic snaps can be placed within reach of the bottom's hand in case the top should have an emergency, although this is not typical.
Panic snaps are also used on certain types of BDSM leather suspension gear for the same reasons as their use with rope. They are sometimes called quick release cuffs.
Note: if releasing a bottom in a suspension situation using panic snaps, the top and/or spotters should be fully supporting the weight of the bottom prior to release. One hand/arm can be used to hold the bottom, while the second hand releases the snap.
Example of suspension cuff using panic snaps http://www.pleasureparadox.com/SR/images/2008%20images/SR-KS0010_Blk_Blue.jpg