While working on a conversation, you might have to make personal notes or loop in your colleagues in a conversation. For example, in case of any technical issue, you may have to loop in a product engineer. In case of a sales query you will have to assign it to a sales person.
In such cases, you can use Private Notes to collaborate with other team members within a conversation. Private Notes will be visible only to your team and not to your customers.
It will also make it easier for your team member to understand the context of the conversation instead of having to read through the entire conversation.