I was sent this cat photo, as a screenshot. However, another image inside this screenshot was the real concern of the sender, an icon.
The icon in question was a parachute. I had to take a few moments to guess what it would be used for.
What do you use a parachute for? Sometimes fun. Mostly, in case of emergencies. What kind of emergency could a file warrant? You could not have it when you need it, and that could be an emergency. Is it for... offline usage?
Bingo. It was. However, that took me longer than it should have to grasp.
In fact, it seems that we are not alone. Google search is very quick to autocomplete the search recommendations for this icon.
I like Dropbox's Favorites implementation in this regard. I like this file, I might need it, it says. Doesn't make you go through hoops.
...and about that tab bar.
There are 6 icons in the top bar. It reaches to the middle of the screen.
iOS allows another bar at the bottom. It even has one in Photos.app itself. The 4 functions at the top bar could just be dropped there, and the file name can then be shown at the top.