Distributed, publicly writable DBMS. I say “DBMS” not “database”, because technically blockchains such as Bitcoin are a “distributed database”. But they are not one that you can create custom tables, indexes, and queries with (e.g. not like MySQL, MongoDB, Postgres, etc).
The “killer app” being that anyone can update the database (subject to permissions) without requiring registration. For example, if creating a Twitter clone: anyone with a SAFE address (and SAFEcoin) can insert a record into the Tweets table, but users can only edit or delete entries that were created by them.
I haven’t been able to determine if implementing one is possible with the SAFE network today. I believe it is technically possible with other projects (cryptocurrencies that support smart contracts). There was a discussion last year about databases on the SAFE network. RDF support seems like it might be able enable this functionality, but I’m not sure if it’s robust enough (i.e. able to discover RDF statements that were created by strangers). A while ago I looked over the code of Patter (it seems to be a similar/compatible use-case), but the program seemed broken to me the last time I tried it.