Append accesses are specific write access which only add information, and do not remove information.
For text files, for example, append access allows bytes to be added onto the end of the file.
For RDF graphs, Append access allows adds triples to the graph but does not remove any.
Append access is useful for dropbox functionality.
Dropbox can be used for link notification, which the information added is a notification
that a some link has been made elsewhere relevant to the given resource.