Twitter is rolling out the option that allows your followers to send private messages to you as well without you need to follow them back. Generally, you can able to direct message someone on Twitter only if he follows you, for follower to DM you, you need to follow that account as well.

Twitter now avoids the second inconvenience (useful for brands) and it is now rolling the option that lets your followers to send direct messages to you irrespective of you follow them or not, but you need to select "Receive direct messages from any follower"option in your account settings for this.

Definitely this is not aimed at individuals or personal accounts, but useful to brands, shopping sites who offers customer care support and need to follow their customers/users back to receive contact details.

Twitter setting receive direct messages from any follower

Don’t try to leave that setting on by mistake, you’ll end up getting lot of spam. If you’ve not this option in your settings means, it is still not yet available for you.

Read: InboxCleaner – Clean Direct Messages in your Twitter Inbox