The company, with many wide ranging subsidiary brands and companies, will give the "lucky" student tools, knowledge and training to search the Internet for links, posts, torrents and information which will assist efforts in bringing cease and desist notices, DMCA orders and other legal means to remove content. The intelligence acquired could also be used later in a court of law if sites do not comply.
to monitor local Internet forums and IRC [channels] for pirated Warner Bros. and NBCU content in order to gather information on pirate sites, groups and activities;
create new and maintain existing accounts on private sites:
scanning for links to hosted pirated Warner Bros. and NBCU content to issue take-down notices;
maintaining and developing bots for Internet link scanning system (see here)
performing trap purchases of pirated products and logging result;
inputting data and other intelligence into "the" (their own) forensics database
periodically producing research documents on piracy related technological developments.
Softpedia suggest a similarity between Warner Bros. and the Chinese government, saying that both organisations look for those who are willing to spy on their peers. Of course, this internship does not necessarily state to spy or collect intelligence on one's direct peers, but as we are all of the same generation of a border-less Internet, we are all a collective here.
Some background information that I have written about before might be of use to students in regards to legalities, illegalities and suchlike. More can be found here.
Torrents are the main issue to worry about. In this context, downloading files through peer-to-peer or HTTP/FTP transfer is "a little illegal", whereas the corporations have a major issue with users who actively share the files. Torrents generally only work on a basis where the files you download are also shared with others to maintain the seed/leech ratio, to enable others to download as you have. These can, and do get tracked.
HTTP/FTP transfers of copyrighted material are illegal, though not deemed as bad as actively sharing content like with torrents. These cannot be actively traced, as such. The only viable way to trace a download from a server like through MediaFire or RapidShare is to seek a court order for the server and/or transfer logs to be sought. A court order can also be issued to your ISP which record every site and file you access, though these are secure and unreadable by the vast majority of ISP employees. This of course is far more difficult to do as some evidence is required before a court order is issued.