What does archive do in personal messages? 

It just keeps the message seperated.  So you would use it for a message you don't want to accidentally delete.  Then when going through to delete old messages in the to me/from me sections you can just select all on a page and delete. 

Adrienne, I'm so glad you asked that! For the Hot Potato Swap, I sent a PM to Jennifer at the beginning with the pre-selected times and for every round, I have been going back through my PM's looking for it. What a pain!  Now I have archived it and can get to it easily for reference.  Thanks to you and Mary for teaching me something new today!