What is the difference between a router and hub or switch?

A router is a more sophisticated network device than either a switch or a hub. Like hubs and switches, network routers are typically small, box-like pieces of equipment that multiple computers can connect to. Each features a number of "ports" the front or back that provide the connection points for these computers, a connection for electric power, and a number of LED lights to display device status. While routers, hubs and switches all share similiar physical appearance, routers differ substantially in their inner workings.

Traditional routers are designed to join multiple area networks (LANs and WANs). On the Internet or on a large corporate network, for example, routers serve as intermediate destinations for network traffic. These routers receive TCP/IP packets, look inside each packet to identify the source and target IP addresses, then forward these packets as needed to ensure the data reaches its final destination.
Routers for home networks (often called broadband routers) also can join multiple networks. These routers are designed specifically to join the home (LAN) to the Internet (WAN) for the purpose of Internet connection sharing. In contrast, neither hubs nor switches are capable of joining multiple networks or sharing an Internet connection. A home network with only hubs and switches must designate one computer as the gateway to the Internet, and that device must possess two network adapters for sharing, one for the home LAN and one for the Internet WAN. With a router, all home computers connect to the router equally, and it performs the equivalent gateway functions.

Additionally, broadband routers contain several features beyond those of traditional routers. Broadband routers provide DHCP server and proxy support, for example. Most of these routers also offer integrated firewalls. Finally, wired Ethernet broadband routers typically incorporate a built-in Ethernet switch. These routers allow several hubs or switches to be connected to them, as a means to expand the local network to accomodate more Ethernet devices.
In home networking, hubs and switches technically exist only for wired networks. Wi-Fi wireless routers incorporate a built-in access point that is roughly equivalent to a wired switch.

What Is a Layer 3 Switch?
Traditional network switches operate at Layer 2 of the OSI model while network routers operate at Layer 3. This often leads to confusion over the definition of "Layer 3 switch."
Answer: A Layer 3 switch is a high-performance device for network routing. Layer 3 switches actually differ very little from routers. A Layer 3 switch can support the same routing protocols as network routers do. Both inspect incoming packets and make dynamic routing decisions based on the source and destination addresses inside. Both types of boxes share a similar appearance.

Layer 3 switches were conceived as a technology to improve on the performance of routers used in large local area networks (LANs) like corporate intranets. The key difference between Layer 3 switches and routers lies in the hardware technology used to build the unit. The hardware inside a Layer 3 switch merges that of traditional switches and routers, replacing some of a router's software logic with hardware to offer better performance in some situations.

Layer 3 switches often cost less than traditional routers. Designed for use within local networks, a Layer 3 switch will typically not possess the WAN ports and wide area network features a traditional router will always have.