This page, available from the top menu once logged in, allows you to backup the entire database to a JSON file. This includes all your categories, and for every file in the database:
The unique ID of the archive (For the more technologically-enclined: LRR uses a SHA-1 hash of the first 500KBs of the file as the ID)
The saved tags
The saved title
This JSON can then be restored in another LRR instance, if it has archives with matching unique IDs.