That depends on your definition of secure.
VPN can provide a secure link over an insecure network (e.g. the Internet) where the transported data cannot be listened in or manipulated by any third party. It's often called an overlay network because it creates a network (link) on top of another network.
The nodes you connect through VPN become direct link partners. That link can be used for remote access into a private network (client VPN), to connect remote networks (site-to-site VPN), or to provide Internet access through a service that obscures your own public IP address ("VPN service").
Since a direct network link is a potential attack vector, both link partners need to either trust each other wholeheartedly or each provide a reliable firewall service on the link. Of course, connecting multiple VPN partners extends the need for trust or a decent firewall.
Routing your (Internet) traffic through a VPN link enables your link partner to examine that traffic. Of course, encrypted data (SSL/TLS) cannot be inspected unless SSL deep inspection is used.