Twitter has enabled a new feature where you can receive direct messages from anyone, regardless of whether or not you follow them back.
The direct message feature is disabled by default, but you can head into Settings > Security & Privacy to enable it. Once you do, anyone can send you direct messages regardless of whether you follow them back or not. If you don't enable it, DMs will continue to work as they always have, requiring a mutual follow to send and receive them. You'll know whether people can receive public DMs based on a new icon on their profile pages with a plus sign.
This feature was initially introduced back in 2013, but pulled about a month after that. It's rolling out to all users, though as with all Twitter updates you may have to wait a while to see it in your account.