You are misunderstanding those articles. They are talking about a physical object that people use to connect their computers and/or access the internet wirelessly.
The reason they talk about routers is because many people do not properly forward their uTorrent port through the router and get slow speeds.
If you do not have a router, then you do not need to worry about that.
In uTorrent go to the Speed Guide (Ctrl+G) and test if your port is forwarded properly.
If it is, the you can use the speed guide to adjust your uTorrent settings for best speed.
See here for more info:
If you fail the port forward test, then you will have to clear the port through your software firewall. There are some guides at the uTorrent forum: