There are two types of interfaces available - detailed and overview.
In the detailed interface, you can see all the chats you have at the moment - active and inactive that you haven't archived yet. You can also see the conversation of the chat you have selected in the middle and on the right side, you can see more information like available quick replies, the screen of the customer in case they have enabled the screen sharing on their side, and more information about the customer like time on site, page visits, current URL, etc.
In the overview interface, you can see all the chats you have at the moment and for most of them, you can see the conversation at the same time, without the need to switch between chats. The quick replies will not be visible, but will still be available if you use the correct keywords.