To delete a conversation, access the conversation by clicking on the Contact icon and click on the contact entry. From there, click on the Conversations tab and you'll see a list of conversation subjects you've had with the selected contact.
Check the checkbox to the left of the conversation you'd like to delete, then click on the delete button.
You'll see a confirmation message appear after you click on delete. Click on yes, delete it to confirm.
Note: After a conversation has been deleted it cannot be recovered.