What is Bit Torrent? BitTorrent is an Internet software protocol that is especially efficient for transferring large files such as music, movies, or video games (and smaller files such as eBooks, too). Unauthorized BitTorrent transfers are sometimes difficult for copyright owners to stop because the complete file is rarely stored in one piece; instead, the file is broken into identically sized pieces that are stored on different computers. The file is reassembled as the user makes a download. Users of BitTorrent sites are usually not anonymous, and IP addresses (the unique numerical address for each computer) can be tracked by copyright owners with access to tracking logs.
Can your college prohibit BitTorrent usage? Your college is free to set standards for WiFi usage and there are many reasons why your school would want to prohibit BitTorrent. The sheer volume of use -- it is estimated that there are a quarter of billion monthly BitTorrent users -- combined with typical mega download file size could tax (or overwhelm) a WiFi provider's bandwidth. (Of course students have workarounds for torrent blocking.) In addition, a college may wish to avoid being liable for its users' activities, for example, if a college student is using his computer as a "client." By making the anti-BitTorrent provision part of the licensing agreement, the university retains the right to turn off the juice to errant users.
Can you/they be legally liable? Yes, those who vicariously facilitate copyright infringement may be liable for copyright infringement. However, despite various legal attacks (including this 2013 case), and despite filing thousands of cases against individual users, the BitTorrent community has so far survived the onslaught of legal enforcement, partially because of jurisdictional issues -- the servers and companies can easily move to a new "cyber-friendly" country. Here's one attorney's tips for fighting a claim of illegal downloading using BitTorrent.