Most p2p networks work in a very similar way. Basically, a user connected to the network has certain files that are "shared" and then other users on the network can search for shared files to be transferred through a direct p2p connection. The problem for many people is that the network is far from private: anyone using the network can access any files stored on the network. Qnext solves this problem by allowing people to creative private "groups" and send files to each other though these groups.
The reason an application like Qnext is useful for the average person is that allows large files to be shared without the use of email, which usually limits its file attachment size. Take a picture share, for example: a user may have large photo files they want to send to another user, files that are too big to send over email. Traditionally in this case the picture share would require an intermediate FTP server where the file could be hosted and downloaded by the recipient. This is how most photo sharing service sites are run.
If, on the other hand, the user didn't want to use a photo sharing service (i.e. that wanted to just quickly exchange the large file), they would have to resort to bittorrent or other p2p software. The problem, of course, is that most people don't want their photos publicly available to the entire world, which is want bittorrent and other p2p networks effectively do.
So Qnext serves an important function by allowing people to share large files privately, without the need for an intermediate server. You can simply drag files from your PC to another in your Qnext group and transfer the file without having to worry about that file being grabbed by anyone else.
With Qnext file sharing, the speed and amount of data transferred is limited only be the sender and receiver's bandwidth and inclination. This has applications beyond simply photo sharing. Basically, Qnext accomplishes what many people usually need a private FTP server to do: exchange large files privately. A company or organization, for example, has a large data file it needs to send to a client. Normally one would have to upload the file to a FTP server and have the client download it, but with Qnext the sender and client can simply establish a peer-to-peer connection and exchange the data.
Qnext is part of a larger trend towards privacy amongst p2p networks. Some of this desire for privacy is due to large amount of copyrighted information exchanged on p2p networks. It is unlikely, however, that Qnext will be commandeered for this purpose: because of it's nature as a private network, it is not searchable in the way open p2p networks are. Qnext remains a useful tool for the legitimate exchange of large amounts of data, and it is unlikely to fall into any danger with regards to software piracy. The very reason p2p networks like bittorrent and like are so successful for piracy is because they are publicly searchable: a massive amount of data can be shared.
The private nature of Qnext means that it will likely remain safe from the eyes of the RIAA and the like, and maintain its reputation as a legitimate way for individual to exchange large files.