The capability to get conversation history over several servers. In Matrix the conversation history is stored by all servers involved in the discussion, and thus it can be retrieved if your own server temporarily goes down. It will also be accessible from all your Matrix-compliant clients, whether they are web or mobile clients.
(edit: disclaimer: I'm also involved with matrix.org)
Hey. Thanks for the explanation.
I ignore the 'will be accessible from all your clients' part - that should be the case for XMPP as well, or will be with MAM [1].
Storing the history on multiple servers? Not sure I understand the use case here (okay 'server goes down' I understand, but spreading my message history to multiple servers for that seems .. unexpected).
OK let me try to explain it better: let's say we have a conversation between 3 friends who are all running their own homeservers to connect to matrix. All three servers will keep a copy of the conversation, and if one server goes down and reconnects, the two other servers can update it with the messages that went on while it was down.
If friend 1 and 2 have a separate conversation in a different room, only their two servers will keep a copy of the conversation history. If friend 3 joins this room, his server will receive the current history from the other servers (there's a limit for efficiency but you can explicitly get all the history via pagination).