A bench vice is a vice that is attached to a bench. When people say vice they are almost always talking about a bench vice. It is a device for firmly holding an object that someone is working on. It consists of two flat jaws--one fixed and the other movable--that can be brought together with a screw mechanism.
Vices exist in a variety of sizes from those designed for the jeweler's bench to those designed for the blacksmith's bench. They are all designed to hold something firmly while it is being worked on. The nature of the worked substance determines the size of the vice. The nature of the worked substance also determines the construction of the jaws of the vice.
The function of a vice is to hold something firmly. This is accomplished by having two jaws that can be brought together with smoothly incremental force, then locked in place. This must be done without damaging the object that is being held. It is also important that the vice hold an object steady while it is being worked on and that is why vices are mounted on benches.
The two main types of vices are woodworking vices and engineering vices. Woodworking vices are for holding wood while it is being carved or planed. Woodworking vices usually have wooden jaws to protect the work object. Engineering vices are for holding metal objects. They are typically heaver than woodworking vices and have rough metal jaws.
Vices come in all sizes. One of the smallest is the pin vice used by jewelers to hold broaches or stickpins by the pin part while the jeweled part is being worked on. One of the largest is the blacksmith's vice (also known as a legged vice) which attaches to a bench but has an extra supporting leg.
The benefits of a bench vice are grip and stability. Grip is so important that stability is sometimes sacrificed--as in the hand vice. This is a small handheld device that exists only to provide a grip on small slippery objects. The hand vice grips the object and the worker grips the hand vice. The stability factor is exactly why most vices are attached to benches.