Do large Minecraft servers run on multiple different machines?

Having played on a number of servers, there are often lingering references to multiple different "servers", or a "server" being down, so you can't play That Minigame You Like today.

Does this mean a large server actually runs on multiple different machines, or is this just some other effect at work?

As far as I can tell, the Minecraft protocol doesn't seem to support a federated or handoff system, but I could be wrong. There are servers with incredibly large population numbers, numbering in the thousands, and this could explain how it scales.

To expand on previous answers, large Minecraft networks can run on multiple servers, however each specific world can only run on one machine. The most common platform to link worlds hosted from different machines is BungeeCord, which is developed by the Spigot team.

Essentially, BungeeCord seamlessly directs you to the next server when changing worlds (such as you would within minigame "hub" style servers) without the need to manually connect to a different IP address. Further information can be found here: http://www.spigotmc.org/wiki/about-bungeecord/

Large scale servers like that will more than likely run off of multiple machines as it is possible through plugins to send a player to a different server. Some servers might use a very powerful overclocked single machine to eliminate players having to connect from server to server, and then isolate players on player lists using various plugins. So to answer your question, yes, they can run on multiple machines, however some don't.