Under MacOS 9 (the operating system my school uses for its Macintosh computers), a drop box is a folder where you have write-only permissions, so once you copy something into this folder, you can't get it out, and they (the owner of the drop box) become the owner of the file.
My school used to use these for students to turn in their computer-related homework with. This practice seems to have evaporated into thin air, partly due to me. Basically, the system was configured so that if you turned in your "assignment", and you notice that you have errors in your project, then you can drop it into the drop box again to correct those errors. So, if one knows the file name, (which some teachers INSISTED on everybody naming their files Grade#-Asgnmt#-Student#), somebody could drop something in the drop box that's EMPTY after a unknowning student dropped it in.
Friends of mine instantly thought of dropping AppleWorks documents with "I forgot the Assignment. Please give me a 0" and putting them in every single possible drop box. Needless to say, most teachers stopped doing that, and just used admin access to get the files directly from the students' "private folders".