I guess this is it

nostr:note1eqmze4t892x99qcukv5kawwu8cr886qxagqsqjdxvefvsmq2c8cshhs7eu

There's a lot of data that could be considered private that you might want to store on relays. The examples given in that particular post are eCash tokens, encrypted to a specific npub, and medical records.

Other examples might be private notes, bookmarks, and virtually anything else you wouldn't want available to just anyone.

Now, why would someone want to store this information on relays, rather than storing it locally?

One reason might be redundancy. These are records you may want to have backed up so they aren't lost in the case of fire or flood.

Another reason might be ease of remote access. Relays can already be accessed by all of your devices, regardless of whether you are connecting via your local network. If you have the know-how, you can also set up a relay that is only accessible via Tor.