A typical connection to a websever is usually done over 2/3/4 ports for a webpage - maybe a few more on rare occasions and depending on your browser settings. Pretty low numbers generally speaking though. Most of the time its pointless opening more as the page is already completed by then.
Torrents on the other hand can open hundreds of ports - If you have a fancy router like the WRT with appropriate firmware, you can login and check this out. Times this by a few users on the network doing the same and the router soon runs out of memory/processing power.
If your on your own network and using Windows you can speed torrents up by applying the TCP/IP patch, as by default windows limits the number of connections to 10 (IIRC).