There are two files lists: local and global. Local files are files that have been uploaded to the conversation you're in. Global files are files that been uploaded to any conversation. From any room, you can always access the local and global files lists.
The local files list is found under the local information section for each room. This will show all files shared in this specific room. Click a link to download the file.
The global files list is located in the expanded menu at the top right of the room. The global files list will display all files across all rooms.