Apple have summarised the process in the help text pretty well. It brings up most of the salient points.
Here's the UI that you get in iTunesConnect during a phased release.
Here's a summary of a few things – several obvious, some less so:
The progress of the phased release is not linear. It is very gradual initially, then ramps up at the end. This means you test the water on day one with 1% of users. The roll out is shaped like this:
If you choose to pause a release, then the interface will give you some further information about this state.
In particular, note that users can still update to this version manually if they chose to. So, pausing the phased release doesn't let you completely stop updates if you find a critical issue with your release. However it should be pretty effective as most users probably don't check for updates manually.
During a phased release, you can create a new update. You can create the update if the phased release is paused.
So, if we create an update B that we see early on in the phased release has critical issues, then we can pause that phased release and create a new update F to fix the problems.
Until F is available, users can manually update to B if they choose to, but most probably won't manually update.
A few remaining points I'll add answers for if I become aware of them.
Is the phasing order by users or by devices? The text mentions "users", but it's not very explicit. If the ordering is by device, a user might have their phone update on day 1, their iPad day 3, their watch day 6, and Apple TV day 7.
Are future rollouts ordered the same way? Or is a fresh ordering picked so that different users go first and last? Or is the order not explicit and just random? In particular, this has implications for a bad release that you are patching with a fix. You might just release the fix if you're sure it doesn't have any problems of its own. But if you phase the fix, half of the users that got the bad release could be stuck with it for a week.