Twitter is testing a new feature that let you choose who can reply to your Tweet and join your conversation. The feature is currently being tested only with a limited group of people globally on Twitter for iOS, Android, and twitter.com.
The feature allows Twitter user to set the reply preferences before posting a tweet. Those eligible to test the feature shall be able to choose who can reply with three options: everyone (the default setting), only people you follow, or only people you mention. Tweets with the latter two settings will be labeled and the reply icon will be grayed