The above photo has been extracted from: Kate Middleton has a baby boy - NYPOST.com
I quote the following from Cambridge Dictionaries Online:"a. To give birth to: She delivered a baby boy this morning."
"formal The princess has been delivered of (= has given birth to) a healthy baby boy."
deliver verb (GIVE BIRTH) - definition in the British English Dictionary & Thesaurus - Cambridge Dictionaries Online
Also, this is from Free Dictionary:
deliver - definition of deliver by the Free Online Dictionary, Thesaurus and Encyclopedia.
The formal announcement " The princess has been delivered of a healthy baby boy" is passive. She didn't do it alone; someone helped the tot to emerge. It's formal because it's meant to sound portentous and momentous.
The semi-formal announcement "She delivered a baby boy this afternoon" is active. It's a simple statement of what happened and tells us all we need to know.
The same goes for the informal announcement "She had a baby boy this afternoon".