Routers

A router, pronounced /ˈraʊtər/ in the United States, Canada, and Australia, and /ˈruːtər/ in the UK and Ireland (to differentiate it from the tool used to rout wood), is an electronic device used to connect two or more computers or other electronic devices to each other, and usually to the Internet, by wire or radio signals. This allows several computers to communicate with each other and to the Internet at the same time. If wires are used, each computer is connected by its own wire to the router. Modern wired-only routers designed for the home or small business typically have one "input" port (to the Internet) and four "output" ports, one or more of which can be connected to other computers. A typical modern home wireless router, in addition to having four wired ports, also allows several devices to connect with it wirelessly. Most modern personal computers are built with a wired port (almost always an Ethernet type), which allows them to connect to a router with the addition of just a cable (typically a Category 5e type). To connect with a wireless router, a device must have an adapter. This is sometimes, but not always, included with the computer at manufacture. Some electronic games, including handheld electronic games, have an adapter built-in, or one can be added later.

Cisco 1800 Router

More technically, a router is a networking device whose software and hardware are usually tailored to the tasks of routing and forwarding information. Routers connect two or more logical subnets, which do not necessarily map one-to-one to the physical interfaces of the router.^[1] The term "layer 3 switching" is often used interchangeably with routing, but switch is a general term without a rigorous technical definition. In marketing usage, a switch is generally optimized for Ethernet LAN interfaces and may not have other physical interface types. In comparison, the network hub (predecessor of the "switch" or "switching hub") does not do any routing, instead every packet it receives on one network line gets forwarded to all the other network lines.
Routers operate in two different planes:^[2]

Nortel ERS 8600

• Control plane, in which the router learns the outgoing interface that is most appropriate for forwarding specific packets to specific destinations,
• Forwarding plane, which is responsible for the actual process of sending a packet received on a logical interface to an outbound logical interface. 
• Cisco 7600 Routers