Federation

Federation in Matrix protocol refers to the ability of independent servers (nodes, homeservers) to communicate with each other. Each server stores the history and state of each room (decentralized conversation unit) and it participates in (such as when a user from your homeserver joins another homeserver), then it shares that information with other servers if required.

This helps to ensure that servers have all the required data and everyone in any given room has the ability to see the complete chat history, no matter what server they're connected to.

Matrix, being a decentralized protocol, makes use of this wherein even if one node goes offline the conversation can continue by connecting to another server, whereas a centralized system would just fail. Once the node goes back online they'll face backfill to sync the data the server missed out on and update its indexes, then the server is ready for normal federation again.