Dropbox avoids having to store multiple copies of huge files by detecting duplicated files, storing only one copy, and letting every user that stores the file download from that one copy. Dropship exploits this system for filesharing by lying to the Dropbox servers and saying that it already owns a copy of the file.
For example, Person A wants to distribute a copy of a CD or something. They upload the file to Dropbox normally. They then use Dropship to create something describing that file, which they then publish. Persons B and C download that descriptor and feed it to Dropship, which tricks Dropbox into thinking that they also own copies of the file. Dropbox then lets Person B and Person C download the file that Person A wanted to distribute, and mission accomplished.