Open: You'll find your active two way conversations in your open folder. If you message a contact directly from the text field on the conversations page, this message will be in the Open filter.
Unread: Your unread conversations will have a notification next to it to indicate the text is new and unread. The unread filter strictly only has conversations that have not yet been read. You can also mark a conversations as unread from your Open filter.
Outbound: An outbound message is a text you've sent out that is waiting for a response. Using an automation from your CRM, or sending a Broadcast message to send messages to contacts will place those conversations in your outbound filter.
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. If you'd like to pull a conversation out of the closed filter, search for that contact on the conversations page. When you select the contact, that will work to place the conversation at the top of your Open filter.