Good question, self! As The Wall Street Journal found out, Twitter doesn't actually care to reveal that information. "[W]e continue to very selectively verify accounts most at risk for impersonation on a one-off and highly irregular basis," reps for Twitter wrote to WSJ in an e-mail.
Which is a nice way of not answering a direct question. Based on the smattering of celebs that the Journal spoke with, though, the service -- which provides verified accounts with a blue check mark -- seems arbitrary at best. Dane Cook said he "hit a few 100,000 followers and one day it was just verified"; Britney Spears' manager petitioned Twitter for the verification; and Sheen, well, who knows? He probably threatened to cut the Fail Whale in half with a samurai sword or something.