The basic idea is this: in an MMO game, situations can arise where your party is the only one in a situation (e.g. Final Fantasy style battles). Furthermore, people in a party may sometimes be physically/geographically near one another - at the same university, for example, or working at the same office.
When that happens, you can 'isolate' that group of players and nominate one of them as a temporary server - turning the game from a high-latency MMO into a low-latency LAN game. So you can have realtime FPS-style battles within the game world.
The major issue is security. If someone hacks their copy of the game and is then nominated as a host, they (or their entire party) could gain unfair advantages - invincibility, choosing the items that monsters drop, etc. The sensible solution, IMO, is a transaction log that the host records and sends to the master server after (or during) the local session. The master server can then check that log for both viability (are players teleporting around? Is that jump a reasonable height? Was that damage appropriate for that weapon?) as well as probability (what's the chances that every member of the party will have scored a Double Star Strike on every one of 20 moves?). If anything looks suspicious the system can flag the log for review by a GM, and action can be taken, from banning that particular account from ever being a host, to banning the account entirely.
Sure, there's going to be a bit of latency there, and if someone /does/ try something they might get away with it for a couple of hours. But I don't think that's too much of a problem.
If you extend the idea a bit, you get database replication. Several of the people here at work play World of Warcraft over lunch. To my knowledge, they meet up in the game world from time to time but spend much time doing their own things. That doesn't mean that one of their machines - the most powerful one, presumably - couldn't replicate data for all of those players.
Of course, at that point it all breaks down because the replicated database isn't read-only. Oh well.