Discussions can be archived one by one or by backing up the complete forum with user data, then restoring it.
Archiving forums may be useful for example if a thread gets too long, if this is the case you can archive it and then start up the conversation again with a good summary overview of the previous threads.
To archive a discussion:
Create a forum named 'Archive forum' on your course page
Go to the forum containing the discussions you want to archive
Enter the discussion by clicking on the discussion name. At the top-right corner of the screen, you'll see a dropdown menu labelled Move this discussion to.
Select Archive forum from the list
You'll now see the discussion in the archive forum. Click the forums link in the navigation bar and select the original forum from the list.
Post a summary of the archived discussion in the original forum to restart the discussion.
Using an archive forum allows you to keep the discussions manageable whilst retaining all the original details.