People online can sometimes be a little less civil than they would be in person, which is probably why Twitter is now experimenting with some settings to restrict who can reply to your tweets. Assuming your profile isn't set to private, people will still be able to see, like, and retweet (with and without comments).
There are three options you can select from, all pretty straightforward: "Everyone," "People you follow," and "Only people you mention." The concept sounded a little strange to me upon first glance, but Facebook offers pretty much the same thing (you can have non-friends react to and share your posts, but not comment).
The functionality is undergoing testing on iOS, Android, and the Twitter website at the moment. If you've been selected for the test, you'll be able to control this setting whenever you're composing a new tweet.
- Twitter Blog