Twitter has begun rolling out a new feature that allows the account holder to let anyone DM (Direct Message) them. Normally only people the account holder follows can start a direct message conversation, that's all about to change though, if you want it.
Fortunately the option is being rolled out set to disabled, so should you want any old Joe messaging you, you'll have to enable the feature first, which by the way is not available to everyone yet.
You can now receive DM's from anyone who follows you, without you following them. Just saw this in settings... pic.twitter.com/Lsf0FR563q— Jim Connolly (@JimConnolly) October 15, 2013
The feature (if enabled on your account) can be found under the Accounts tab.
We can't think of a reason this might be beneficial to the average user, it could even open yourself up for a lot of spamming; but as Connolly points out, this could be a great feature for businesses allowing customers to privately message the account holder for advice or other questions they would not otherwise want shown publicly.
Source: Jim's Marketing Blog