Tim Pool recounted how his account got verified a few days ago: https://www.youtube.com/watch?v=67nFNUPQaeI&t=1m25s.
TL;DW: His employer, VICE, instructed Twitter to verify him, and they did.
Ultimately that's what this badge comes down to: for most people it's a mark of being on the inside, knowing the right people. The right agency, the right employer, maybe just having a friend working at Twitter. There are some other certain criteria that aren't publicized, and they have in the past randomly given it out to "high profile" people on Twitter, even though that seems to be totally random as well.
This is a special club, Twitter has on and off said it means many things, but there's no consistency. Just like there's no consistency with how they enforce their rules, there's no consistency with this special privilege either.