First this questions and ans is not related to OpenStack. This is purely networking fundamentals. Private network is subnet created for vms to communicate each other in that subnet. E.g 10.0.0.x is your internal IP address.

Public IP address is for IP address assigned to vm which is accessible from out side the vm network. E.g you may have external network with 192.168.0.x as network for your desktops. This IP can be assigned to your vms. In this case vm is also accessible from outside. This is public network. It is as good as your vm having two interfaces with two different IP addresss. One IP address is internal network. Other one is external network.

Hope this clarifies.