Router

Routers receive packets and looks at the destination of each packet and forwards them based upon their layer 3 address, usually an IP or IPv6 address.  Routers can sometimes perform both routing and switching functions.  A router is required when two devices on two separate networks are required to talk to each other, such as devices on a LAN (Local Area Network), and the internet.

Switch

A switch typically exists on a LAN (Local Area Network) and usually forwards traffic based upon MAC addresses from one port to another.  Switches are increasingly able to perform routing functions.  Switches can operate on one or more layer 2 domains, or VLANs.  A switch is usually what an endpoint such as a computer or VoIP phone will connect to.