Basically it opens when a request is called and closes once the results have been disposed or consumed. You can manually open/close or use the same connection using the object context…
This article has a more complete explanation –
http://msdn.microsoft.com/en-us/library/bb738582.aspx (archive.org)
Here is the How To on using an entity Connection –
http://msdn.microsoft.com/en-us/library/bb738461.aspx (archive.org)