In the Advanced Options for a user under the Users & Groups System Preference, there is field for UUID and a button for Create New next to it. How is the UUID used by macOS and what are the implications of changing it?
The UUID (aka GeneratedUID, so Google that one instead) is used by Open Directory Services on macOS X. You can see this and more using the macOS app Directory Utility. Read more the book Apple Training Series: Mac OS X Directory Services.
Ownership and Permissions problems would result from a change of UUID. Not just regarding files and folders, but other data such as that in Calendar.
PS: I no longer see the Create New button in High Sierra.
Sounds like main consequence of changing UUID is messing up Open Directory. As Matt noted it's not changeable in High Sierra and later.
If you want to see more interesting aspects of Open Directory management, start up "Directory Utility" on macOS and browse Name-Value pairs for your macOS account. You'll set the GeneratedUID there and you can copy/paste it.I think you can even edit it in Directory Utility even under Mojave, but I have no intention of testing that.