Most of the changes can be seen in this one screen shot:
So the first thing to note is that conversations now have their own tab, which allows us to give a few additional navigation links to specific lists.
From there, you'll note that conversations can be starred. You can see the conversation listed there is starred. Starring works like you're probably used to in emails; it's mostly to allow filtering.
You can also bulk manage your conversations (over multiple pages) using the inline moderation-style check box. You can star/unstar conversations, mark conversations as read/unread, or leave conversations with this.
Finally, you'll note that all participants are listed on the conversation list. They are also listed on the conversation popup. (Note that to enable this for existing conversations, you will need to use the conversation cache rebuild option after upgrading.)
Oh, and it's been there for a long time, but did you know that you can filter conversations by starter or participant? Click the "conversation display options" button. Go ahead, try it here now.
This is by no means the end of the line for conversations and we still have plenty of ideas to look into for future versions.