A DM "home screen" of sorts for them to have up when not in an encounter. It would include things like the game log, the ability to roll, and the ability to search in the various lists (like inventory, extras, spells) to quickly reference information. In short, it is the hub for running your game.

Pretty much what I would love is a page that I would be on for most of the game where I can pull up important info (like wild shape stats or a monster's info), roll dice, see my player's rolls, and enter encounters when necessary, in addition to whatever features a DM may wish to add (It could be like a template where you can include or remove various windows and features). 

I love it.  
I would like to be able to reference commonly used tables, like a list of conditions... or combat modifiers.
Being able to go into an edit mode where you can drag and drop things would be nice.
Tabs for having multiple views (combat cheat sheet, travel cheat sheet, social cheat sheet, etc) would be nice too.
Custom boxes with a small text editor to create your own notes/tables would also be nice.

Yeah, feature creep, I know.  But you know, us DM's, we need some love too.  Digital DM Screen for the win!

I want a little "sticky" for each player in the campaign with their passive perception, HP, ac, etc. like I use on my physical DM screen

I want a [DAWN] button on the DM’s Screen to refresh magic item charges in the campaign.