It appears to be several popular programming fonts with a bunch of extra glyphs added. Does Vim require special font support, because I'm having a hard time figuring out the point of this.
Is this for people who like to put icons into code comments?
Powerline/Airline is one big one -- the status line in Vim is just a character-mode thing, but with a few extra glyphs (for line number, git branch, and arrows/wedges, most notably) it looks a lot better than if it's using a more limited character set.
vim-devicons is the other big one that this is supporting, which gives you filetype icons.
Are these things huge big deals? No. Are they nice things that make Vim's UI look a little cleaner and more informative within the confines of a pure character-mode application? Yes.
No, there's plenty of reasons why you'd want more characters available. I use emoji for git diffs in my vim line number column, for showing battery status, audio levels, etc in tmux, and so on.
Not really, that's the terminal emulator's job. If you want to use unicode fuckery for pointless hipster icons, you just need to have the glyphs in any installed font, and the terminal should substitute it when needed, no matter what your configured default font is (unless said font also provides the glyphs).
I get it, you don't like the pointless icons. Some do. Often when having a homogeneous naming structure with long filenames in NerdTree, it's nice to be able to say, "Oh this is the CSS file" without having to hit a capital A to expand the "drawer" to see what type of file it is. For the record... I don't own skinny jeans, and I'm probably far too old to be a hipster.
Is this for people who like to put icons into code comments?