Update: It appears apps are no longer able to bulk-delete contacts on iOS. We're looking into alternatives. In the meantime, if you sync your contacts via iCloud, Google, Outlook.com, Yahoo!, or another service, you can open them up on the web or on your Mac or Windows PC and more easily bulk edit there.
By default your iPhone will only let you delete contacts one at a time, which isn't a very pleasant process for anyone who has lots to delete. For those that don't want to go the nuclear option of deleting all of them via iCloud, these is a way to delete multiple contacts at once, you'll just need the help of an App Store app to do it.