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At it's simplest, a router acts as a data dispatcher, choosing the best path for information to travel so it's received quickly.
The most familiar type of routers are small/home office routers that simply pass data, such as web pages and email, between the home computers and say a cable or DSL modem, which connects to the Internet. More sophisticated routers range from enterprise routers, which connect large business or ISP networks up to the powerful core routers that forward data at high speed along the optical fiber lines of the Internet backbone.
And then there is this distinction between switches and routers:
Here's a good place to read through some router-related news: