It will send you notification when there is an update or more information available. You usually get a small popup box when this happens. It means you don't have to open the app to see what is new. It's not very intrusive, so IMO it's quite useful, but some people may not like it.
Edit: I should have mentioned - if you enable push notification and later decide you don't like it, you can disable it in your Settings, so you won't be stuck with it irrevocably.