Why is my laptop still connected to the internet?

On my router, when something is using the internet, it shows how many open sessions there are. Typically I find there to be between 10 and 30 open sessions when I'm using the internet to browse, look at movies, and whatever else. I know computers stay connected to the internet when off, but very minimally.

My laptop is off right now. I disabled the wireless internet on it before I turned it off as well. According to my router, it says my laptop has 70 to 80 open session currently. Usually only goes that high when I start using torrent software. Turned off, a computer doesn't use many more than 5 open sessions.

My questions is this: Why does it say my laptop connected with the internet with over 70 open sessions even though it is turned off? Is it possible someone's bouncing off my laptop's signal to connect to my internet? If they are, how can I fix that so they aren't?