Wide Area Network (WAN) connection refers to data connections between offices. It allows offices to share resources, for example a file server, at one location could be used by two different offices.
A WAN connection can either use the public internet together with a VPN, or use dedicated data connections.
The option of using the public Internet together with a VPN (virtual private network) is always cheaper as you do not have guaranteed bandwidth on the public Internet. From a provisioning perspective you order an Internet connection (see list item 2) from a broadband provider, and then you need your IT provider (many broadband providers can assist too) to configure a VPN between your sites (see list item 3).
The option of using dedicated data connections requires ordering of private network connections from your telecoms carrier or broadband provider. For example, private ethernet services provided by Telstra (Australia), Colt (UK), and Verizon (US).