Facebook's (lacking) explanation is here:
developers.facebook.com/docs/reference/plugins/live-stream/
The idea of LiveStream is to have a 'discussion' on your site usually at a specific time about a specific topic. Examples would be "Chat with the admin at 7pm" or "Watch/comment about the football game together". In each case, you would generally want to set up a time on your site for everyone to go to a specific page and then have a discussion or interview about a specific thing. When orchestrated well on the right type of site or event, it can work out, but in general, unless you're planning activities like this that you want to promote, I'd recommend using the Comment box on pages for 'static' conversations.
I don't know how long the discussion is kept in the LiveStream. It seems to be a 1-3 days, but I haven't narrowed it down.
Hope this helps with an explanation, but if there's more we can add, let us know!
How long do Live Stream comments stay there?
