We are used to the term "PM's" (private Messages) from the old forum.
With the new software they are called "Conversations" now and much easier to handle. They work and show like a "thread" but they are private.
Means only you and the recipient can see it. For example you sent a "PM" to somebody and he replies you don't get another "PM" anymore but you will see a reply in your private thread.
This means less clutter in your inbox. In the past when PM's went back and forward you would see tons of different PM's all regarding the same topic. If you would sent a "PM" to several recipients they ALL participate in the same private thread and you all see who replied what.
Now you don't have to sent your reply to all the recipients as they are all included in the private thread.