Projects have a tool called "Files". When this is added to a project it enables files to be uploaded to a project.
To upload a new file click on the "Upload New File" button on the files page:
You'll then see a pop up:
On the pop up you can drag and drop multiple files onto the dropzone to upload. Or click the dropzone to open your computers file chooser.
You also have the option to attach a file to a task that's part of the project you're currently in.
When you're done hit "Upload & Save" and your files will show in the files list.
From here you can filter, sort and group your list as normal.
Your files will also show in the master files view that you can get to from your account dashboard.
A few points to note:
People will only see file from projects they have access to.
People who have a role that doesn't allow them to see tasks won't see files that have been attached to tasks.
If a task has a "Creators Only" privacy then people with a "Collaborator" role won't see any files attached to that task.