Under the hood, scuttlebutt uses multiple independent blockchains, each tied to a single user. The upside of this is that it makes for a great eventually consistent gossip protocol; the downside is that the entire chain needs to be propagated for any of it to make sense, making it a very storage-intensive protocol.
Private messaging is implemented in a really interesting way using cryptographic envelopes that are publicly gossiped, but only decryptable by the recipient — whose address is also encrypted and therefore hidden.
Personally, I'm looking forward to when they introduce a good decentralized solution for moderation. This would help keep the size of the chain smaller, and make the information you see more usable.
The Scuttlebutt Protocol Guide [0] is a really easy and interesting read, I highly recommend it.
[0] https://ssbc.github.io/scuttlebutt-protocol-guide/
Edit: clarified what Scuttlebutt is.