Since Twitter launched the only way for a follower to be able to directly message you was if you were also following them. Twitter has now unveiled a new option that makes it easier for followers to directly message you. The new setting has reportedly been rolling out over the last week.
Users can now check a box allowing any follower to send them a direct message without having to follow them. A note along with the option reads:
Generally, you must follow someone before they have the ability to direct message you. If you check this option, any Twitter user that follows you will be able to send you a DM, regardless of whether you decide to follow the back.
The intent of the new feature is to allow businesses and brands using Twitter to receive messages from followers. Before this feature was enacted, the brand and business pages would have to follow all of their followers to allow direct messages. Allowing direct messages from anyone will certainly make maintaining brand or business pages easier to do.
The direct messages option can be enabled from the main settings page on twitter. The rollout is happening in a staggered fashion so all Twitter users may not have access to this feature at this time.