A router is used to finish edges and given the right bit, a router can plane edges, cut multi-curved mouldings, produce relief panels, rabbet and dovetail for professional joints, trim formica and cut delicate grooves for professional inlay work.

link Basically a high speed motor with handles and an adjustable base with a collet that accepts profile bits to cut dados, rabbets, or shapes.

In its simplest form, a router is just an electric chisel. But it's one of the most versatile power woodworking tools around, able to plane, saw, shape, groove, mortise, trim, dado, and more. It's usually operated as a handheld tool, but it also can be mounted to a stationary table for even greater versatility. Home Improvement Encyclopedia

A tool with a large motor and a collet chuck for holding router bits, with a flat bottom for accurately guiding the tool over wood to make grooves or carve shapes along the edges. The similar product for metal is a mill which is a heavy duty chunk of hardware to apply the forces needed to cut metal accurately, usually with a gear driven moving table.

A tool used in cutting a groove or chamfer.

A power tool that is shaped like a cannister and has a bit protruding from the bottom. A router is used to do such things as making grooves, dadoes and rabbets, and mortising door hinges.

Woodworking tool with a high speed bit for cutting rebates, dadoes, insetting butts, and forming decorative or rounded edges.