Complex sentence: The VPN connection across the Internet is technically a wide area network (WAN) link between the sites but "appears to the user" as a private network link--hence the name "virtual private network".
Split into simpler sentences: The VPN connection across the Internet is technically a wide area network (WAN) link between the sites. From a user perspective, the extended network resources are accessed in the same way as resources available from the private network--hence the name "virtual private network".