basically, a router is a pc
if you class a 'port' as a door
without a router, all the 'doors' lead directly to your pc, so the firewall of your pc will get all sorts of people knocking on the door, and you decide (using the firewall, who you let in)
with a router, it's a pc that isn't effected by the nasties that bang on the door all the time, and will ignore them all and only let people in that you've invited -ie, playing on a game server, or a website that you've asked for data from..
you can configure the router to leave a door (port) always open directly to your pc, where your pc firewall will deal with it -ie, forwarding a port for utorrent to get maximum speed, or for remote desktop ability etc..
in short, your linksys will be blocking all by default
so having a router, instantly blocks about 60,000 ports, if everyone had a router, things like the blaster virus would be useless