I know this feature is sort-of available on mobile (iOS and Android) but I haven't seen it yet on Desktop, which is what I almost exclusively use Any.Don on.
I have a lot of tasks that need to be done on a monthly basis but I often end up waiting for someone else before I can knock it out. I think it would be handy to have a snooze feature so tasks that I simply cannot do yet I can hit "snooze" on until the other person is done. It would move the task into the list for the next day and clear it out of today's list. That way I know I checked in on it, determined I was still waiting on someone else, and can confidently move onto the next items in my list without constantly checking in.
Ideally the items that I hit "snooze" on could have the option to go into their own list - not necessarily a "tomorrow" task, but also not really a "today" task anymore. Maybe they could be "un-snoozed" if something changes and now I need to make sure to touch on that task again today, but I can't interrupt what I'm working on.
The feature could also include a place to add a note as to why the task is being "snoozed".
And it doesn't have to be labeled "snooze", it could also be "delayed" or "pending".