A machine shop is any workshop that extensively uses mechanized tools, usually to craft and shape metal. With a full array of machine tools on a workbench, a machine shop is able to accurately and precisely cut metal to shape, carve shapes and details, or plane metal to a level surface.
One of the primary tools used to cut metal, bench mills come in two types: vertical and horizontal. Both work in essentially the same fashion, using a manually controlled drilling and cutting bit to shape material. A good startup bench mill should be able to cut slots, plane and drill holes like a drill press, with manual controls that allow for precision movement of the material along all three axes.
Lathes are cutting devices that spin material rapidly around a central axis and cut (or sand) using a stationary blade. Leadscrews allow you to set the depth at which the blade cuts, and should also allow for completely manual, free-hand cutting. Lathes are essential for cutting threading into material to be mounted using bolt-and-nut fasteners, as well as an essential work piece for shaping metal.
A bench vise is a clamp that affixes to your workbench by screws, allowing you to hold and position material as you work on it. High-quality models provide a lockable swivel function to rotate the clamping arm to the angle at which it's easiest to work. Vises designed specifically for metalwork will feature rough jaws, while combination vises' jaws are curved at their ends to grip pipe and other round objects without crushing them in a flat gripping surface.
A bench grinder mounts to a workbench and provides a pair of rotating grinding surfaces used to roughly shape or polish material. One grinding surface is a traditional grinding wheel, used to sharpen and shape metals, while the other is a wire brush used for the first stages of polishing metal surfaces.
Similar to a lathe and a mill, planers are used to shape metal as it passes underneath a stationary blade. Unlike lathes, a planer's movement isn't rotational, and instead of a cutting bit as used in a mill, planers cut with a blade. Operators use planers primarily to cut very flat and level surfaces quickly.