First, businesses can now add a “send a private message” button to their tweets. So you might start a conversation with a business via public tweets, but at a certain point they can ask you to move to direct messaging with just a single tap or click. Second, Twitter is adding an option for businesses to privately ask you for feedback after a customer service interaction.
Now, I can imagine that this would be appealing to companies who’d prefer to discuss customer issues and complaints privately, rather than seeing them broadcast for everyone to see. However, Twitter identifies some other advantages to these new features.