Like a DMZ a VPN is a security concept, it is not a protocol (like SSH) nor a certain software package. There are multiple software packages available to set up a VPN between two or more hosts. They all use the client-server model and usually are incompatible with one another. Have look at the OSI model and make yourself aware that the encryption can be applied at different layers of the communications stack. VPN generally relies on cryptography, thus you may be interested in Cryptographic hardware acceleration and setting up Random generator.

The VPN server running on your router can provide a secure connection to your home network while you're away. If you need to access the router itself or any of your home network devices from afar, the VPN server is a great solution.

You may want to run a VPN client on your router to encrypt your connection to the internet and prevent your ISP from snooping on your traffic and DNS requests (which in some countries is now legal for ISPs to monetize) as well as meddling with DNS requests or HTTP traffic. In order to use a VPN client on your router, you would need to obtain credentials to a corresponding VPN server. Your connection to the VPN server is encrypted, preventing your ISP from snooping/meddling on your traffic. A wide variety of commercial VPN providers exist. Once you install/run a VPN client on your router, it's best to route all your traffic via a VPN tunnel.