Deleting a Conversation
After checking the box you will get a popup.
Simply click 'Leave Conversation' or select the drop down menu for more options, you can select ALL your conversations to edit by checking the 'Select All'.
You will then have a choice to accept or ignore. By accepting this means that if any parties involved in the conversation can 're-open' the chat with you instead of creating a new conversation. Ignoring future messages they will need to create a new conversation with you.
The other way to delete the conversation is when you have opened the conversation is to simply select the 'Leave Conversation' option just under the title.