Specifically, this solves the problem of data consistency across different node/peers without needing a central (ie, Facebook's servers) master.
The way it works, is like so: http://gun.js.org/distributed/matters.html
However, a blockchain is still actually useful for a P2P Facebook. A blockchain that uses a consensus algorithm (PoW, PoS, etc.) is not scalable enough, though. But that is okay, as we do not need to solve the Double Spending problem for tweets/photos (see the previous link as to why).
So what does a "blockchain" mean then? A blockchain is a cryptographically signed linked list, often a DAG (Directed Acyclic Graph). But these graphs would more likely be social networking data, which is naturally a graph - and they would be signed with user's public/private key pair.
Solving for that is pretty easy, we already have it working:
http://hackernoon.com/so-you-want-to-build-a-p2p-twitter-wit...
And our goal is to build a social network that has distinctly different properties than Facebook, one that is based on psychological research and emotional intelligence:
https://hackernoon.com/a-new-kind-of-social-network-emotiona...
Finally, the hardest factor is to remove the complexity of cryptography. There turns out to be a good security standard that lets user emulate username/password combos (see the middle link for more details), in summary:
You use PBKDF2 to extend a user's password with a salt, this creates a Proof of Work which is used as an AES symmetric cypher key to decrypt their private key. Fully P2P, but with a traditional UI that users understand, yet PBKDF2 makes it impractical for a cracker to guess (or even a dictionary attack) against the user's account.