If you think about the sheer volume of Backups... Let's say there's 30 million iOS5 users (who have downloaded and updated to iOS5) times an average of 10GB per backup... That's an insane amount of data to be thrown at Apple at once...
I'm hoping the reason is that they're staggering the inflow of data. I don't know of another time in history that this much data has been sent towards a company, it's usually streamed from it.
The backups should be less than 10Gb for almost everyone - remember, all the apps and music are already stored on Apple's end, it's just your personal data, photos etc being backed up - but yes, even at 1 Gb each and 1m users trying to enable it so far, that's a whole petabyte of data hitting them ... enough to max out an OC-192 connection for about two weeks. Must make for some interesting traffic graphs!
The downloads will have been even greater traffic - that all gets cached and load-balanced by Akamai, so the thirty petabytes of download traffic was "only" a few terabytes downloaded from each of 10,000 servers, but even there Apple's servers managed to break quite badly for a while last night.
On top of all that, presumably they're migrating a lot of data from MobileMe over to the new iCloud systems right now, which won't help the load.
The "Lion recovery" update broke my MBP to the point of having to reinstall - which is fortunately very very simple now, but still takes about two hours of waiting and downloading - and iOS 5 failed to install the first ten times I tried, but worked first time this morning, presumably because the initial surge of requests was cleared. I imagine iCloud backup will be much the same: tonight or tomorrow, it'll start working fine.