Twitter can be a fun place to share and interact with your fellow humans. However, it can also be a wretched hive of scum and villainy. That's why keeping your Twitter direct messages open is a bit of a risk, but Twitter is rolling out a feature to keep the riffraff at bay. Soon, all DMs from strangers will be segregated from the messages you care about.
The change to DMs only applies if you have your account set to allow messages from people you don't follow. If that's the case, new direct messages from these people will start going into a separate "Requests" tab. You can check the conversations there at your leisure and either accept or delete them. Accepting a request allows that person to send you DMs that appear in your main inbox. DMs from those you follow will still hit the inbox as normal.
— Twitter (@Twitter) May 30, 2017
This change will only be visible in Twitter's own products, like the official app or website. It's unclear if developers will be able to implement anything similar in their third-party apps.