A router is a device on the network or sometimes software that determines that destination of a network packet and is be connected to atleast two networks. It determines the way send each information packet based on its current understanding of the state of the networks it is connected to.
A router is located at Gateways and is usually accompanied by a Switch. A router may create or maintain a table of the available routes and their conditions and use this information along with distance and cost algorithms to determine the best route for a given packet. Typically, a packet may travel through a number of network points with routers before arriving at its destination.