Conversations with unread messages are denoted by an orange highlight with an orange dot next to the contact's name in the middle panel. When a user clicks on the conversation and scrolls through to the last message, the conversation is automatically marked as read for all users that have access to that contact.
Messages are marked as read on a conversation basis, not on a user basis - once a user clicks on a conversation and it's marked as read, the conversation will appear as read for all other users with access to that contact.
The orange dot indicates that there is an unread message for Beatrice Hunt, and we've clicked into that conversation. We'll scroll down to the newest message (the Scroll for more notification on the conversation lets us know to scroll for new messages). Also note that the icon in the top right corner has bubbles to also label that message as unread.
The orange dot has disappeared from the conversation in the list view and the icon in the top right corner now has a green check mark, indicating that this conversation has been read.
In addition, multiple conversations can be marked as read at the same time. Within the conversation panel, check the boxes next to the messages you want to mark as read and use the dropdown menu at the top to perform a bulk action.