By default, in order to send a direct message (DM) on Twitter, the tweeter must be following you. It’s a handy setting that helps cut down on “silent” spam. But businesses—especially online store owners—should consider checking the option to allow anyone to send you a private tweet.
While you may open up the account to some additional, unwarranted private messages, allowing visitors and customers to contact you privately can help avoid damaging tweets. People who want to advise you of issues outside the public eye, especially if they’re savvy on social networks, may opt to contact you privately, opposed to having all their followers (and yours!) from witnessing rants and suggestions.
To turn this feature on, visit your account’s settings (click the gear icon), and check off the box next to Receive direct messages from any follower. Be sure to click Save changes!
If you find the account receiving too much spam messages, you can always turn this feature back off. However, much like email, blocking DMs from current and potential customers may come at a cost.