Could be a number of things. I just had to deal with this big time so I'll tell you all the things that I tried before my internet speed improved.
As someone above said, it could be that not enough people are uploading your torrent, making it slow to download. Check your internet speed to make sure that it's slow, not just the torrents.
http://www.speedtest.net/
My internet speed is 30mb/s when it's working properly.
COMPUTER PROBLEMS:
First off, make sure that the torrents you've downloaded are not "seeding" or uploading to other people. Whenever I get done downloading a torrent I immediately right click it and pause/stop it from uploading, then I delete it from the list of torrents so it wont start automatically uploading next time I open up my bittorent client.
Your computer could have programs running in the background that you may have accidentally downloaded. Check your installed programs and uninstall anything that looks fishy.
You could have too many programs opening on start up, disable as many programs from loading on start up as you feel comfortable with. If you don't recognize the program search for it on the internet plus the words "start up" to find out what it does.
Another problem if you have other computers in your house they could be weighing down your internet speed with the same above problems.
****After I did all this I bought a new expensive router, wider range, and STILL had problems.***
ROUTER PROBLEMS:
If you have no other computers, make sure your router does not have a "guest access." People living around you can be automatically joining your network via your guest access. Delete it if you have one. My internet speed immediately went up after I did this, but it was still slow.
Next, change your password to something secure so no one can use your internet connection.
Make sure your router is not around other things that make signals (x-box wi-fi, cordless phones etc) including microwaves in use. make sure no chargers or anything is sitting on your router cords. Give your router some space, the closer your router is to your computer the better.
Your router signal can be on the wrong channel. When I checked what channel my router signal was on I saw that there were like 7 different routers in the neighborhood using the same channel as mine. I moved it over to a different channel with less people and it helped my internet immensely.
CABLE INTERNET PROVIDER PROBLEMS:
If nothing is working yet, your cable company could be making the problem. When I had issues I called my cable company and they said they were sending a weak signal. They sent someone to my house to fix it and he noticed that my internet modem was old and they replaced it with a newer one. This helped.
Turn off your modem/unplug it and remove the battery for at least 20 seconds so it can fully reset. Turn off your router as well, unplug it. Reconnect both of them. This is usually the first go-to fix for most people and solves most internet problems.
EVERYTHING FAILS?
If you directly connect your computer to the router via the ethernet cord your download speed should shoot up. You can do this if nothing else works and you really need your download speed.