Open: You'll find your active two way conversations in your open folder.
Unread: Your unread conversations will have a notification next to it to indicate the text is new and unread.
Outbound: An outbound message is a text you've sent out that is waiting for a response.
Closed: A closed conversation means you have ended your two way conversation and once you close the message thread it will go into the closed folder. You can reopen the conversation simply by responding to the last text.