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On why using a home router is better than connecting your PC directly to your ADSL or cable modem.
When you type something into Google it's a bit like writing your question down on a bit of paper and putting it in an envelope. On the front of the envelope you write "Google Inc." so the postman knows where to send it and on the back you put "6 Anyold Road" as your return address. When Google Inc. get your letter they write out the answer, and send it back to you.
If you connect a computer directly to the net without a firewall, it's a bit like opening every single bit of mail you get—quite a lot of it unwanted but some of it dangerous.
If you use a router it's a bit like having someone check incoming mail and only passing it on to someone if it's specifically addressed to them. More than that, knowing that Bob has recently sent a letter to Google, our private mailman knows to expect a reply. Anything unexpected can also be thrown away unopened.
On using a router
In a large organisation that is constantly in touch with its field sales team, its suppliers and customers, it may have a choice of different delivery companies. Some delivery firms may be cheap and quick but only deliver locally; some may be more reliable and give insurance cover but be more expensive; others may only cover certain types of goods. So on the wall in the goods outward office is a piece of paper that tells the staff which delivery firm to use for which goods or destinations. In a computer network where there is more than one route that the information can trave across, the box that controls which route to take is called the router.