Play with your friends
Larísa nailed this one in her comment to my previous post. You start playing an MMO with a couple of your friends or alone and then, later, you meet other people that play the game as well. Obviously you'd like to play with them (and show them your uber leet gear) but you can't because they play on another server. In WoW's case you could go and pay some money to Blizzard to transfer your character but would then in turn not be able to play with any of your friends on your old server anymore. If you played on one big server (with Aion-like channels to avoid overcrowding) instead, you could just play with whomever you want.
Find a new home
My guild sees a fair number of applications from people who wish to transfer to our server because they don't want to stay on their. Maybe there are no guilds good enough for them on their server or maybe it is totally dominated by the other faction. Maybe their server has a low population and it's impossible to get PuGs going. Whatever it is, it prevents these people from finding a place that feels good to them and forces them to pay for a character transfer that might not even get them what they are looking for. In a single-server world, other communities are just a mouse click or three away if you don't like yours.
Niches
A large population of players allows for many more niche interests to be fulfilled. If only one in five thousand players is interested in your all naked Molten Core run it is very unlikely that you'll manage to get a raid together on your server. If everybody was on one server, you might just find more sickos like you. In a similar vein, the right guild for you is very likely to exist and the economy could support many more niche products. Chris Anderson's book The Long Tail tells us that with the internet reaching so many people, almost everything can sell. Similarly, a huge server population would allow for a game to have a much more diverse crafting and loot system while still supply and demand in balance.
Put the Massive back in MMO
Players in current MMOs, especially on matured servers, tend to be concentrated in very few parts of the world. It's not uncommon for me to be the only player in the night elf capital city of Darnassus or its space goat counterpart Exodar. A dynamic channel system (see part three when it's done) could put all the players in low population zones into one channel, making those zones feel less empty while still keeping the more popular zones from overflowing.
Huge servers also allow for massive events in theory, but practice has shown that the technology can't really support hundreds, let alone thousands, of players in one spot.
Balance
I've heard of World of Warcraft servers (or battlegroups these days) where Horde always wins normal battlegrounds but Alliance always wins Alterac Valley and vice versa. I've seen people server transfer to be on a server on which their side has an advantage. I've seen people transfer away from servers because one faction had an absolutely dominating number of players while the other had almost none. Aion artificially enforced that balance by forbidden the creation of certain faction characters on imbalanced servers.
Now, there's always a chance for such imbalances to appear, but they are far less likely if you have one big pool to fish from instead of many small ones. If you grab two M&Ms randomly from a bag, the chances that they have the same colour are way above zero. if you grab fifty instead, it is highly unlikely that you will get such an imbalance.
Design opportunities
With such a large amount of people at their fingertips, designers can do much more than with just a few. Imagine a PvP battle that is designed to be a week-long struggle for control of terrain with a fortress or something to defend on each side. In a multi-server game, nobody would be defending their side's castle at night and a few people logging in at five in the morning could simply win the whole battle by themselves for lack of defense. With one massive server, there will always be people online to play. You could imagine various other gameplay elements that rely on having many players available.
I'm sure I missed some points here, do feel free to add to this. Part three will likely hit on Monday with ideas on how such a huge world could be set up.
