What is a Django "app" supposed to mean?

There's a distinction to be made between reusable apps and non-reusable apps. For reusable apps it's essential that they offer well defined functionality and are intended to solve a well defined problem. If this wasn't the case, they wouldn't be very reusable.

However you're likely to also have some non-reusable apps, i.e. one or more apps in a project that implement application logic that's specific to the project. In my projects I always have a non-reusable app called core that acts as glue and ties everything together. If I have distinct sections in my site I may choose to have more non-reusable apps, because I like the way it essentially namespaces my project (e.g. models, views, templates, etc.)

A Django app is a group of related functionality used to complete or maintain one aspect of a site. The web application you describe would be separated into at least 2 Django apps, depending on how granular you want to make the handling of the uploaded files.