Depending on which direction you swipe a message conversation or a particular reply will determine what you can do.
Table of Contents
Swipe Conversation
Swiping a conversation to the left allows you to mark the conversation as unread.
Swiping a conversation to the right allows you to mute a conversation or delete a conversation.

Muting a conversation means you won’t get a ‘ding’ or vibration when a new message is added to the conversation. You will still get new messages, just no notifications.
Deleting a conversation does what it is – mostly. If you tap Edit near the top you can Show Recently Deleted.
From there you have the options to Delete, Recover, Delete All or Recover All.

Swipe Message
You can swipe a message within a conversation left to reply to that particular message no matter where it is in the conversation. If you decide you do not want to reply to a particular message, then tap anywhere outside of the response.
You can swipe a message within a conversation right to see when that particular message was sent.

With that said, keep on swiping in the free world.