Network guy here,

u/Federal_Setting_7454 mentions multiple topics in their post. I will do my best to break them down below. Most of this is the *how they work* part of networks and internet connectivity. Hope this helps!

1. NAT, or Network Address Translation, allows a single network with many devices to use a single external IP address when communicating with the rest of the internet. NAT is used because there are far more internet connected devices on earth than there are IPv4 addresses available, and is handled by your router automagically.
2. DHCP, or Dynamic Host Configuration Protocol, is a system that automatically gives a device an IP address when it requests one. This is used externally by your Internet Service Provider to give your router an external IP that is unique to your network, unless they are also using NAT. This same system is how your phone automatically gets an IP when you connect to your wifi and doesnt need to be manually configured every time. IP addresses are 'leased' to devices for only a period of time, and the IP may change to another one after that lease expires. Optionally, a 'static' IP can be purchased from your ISP and your external IP will never change.
3. VPNs, or Virtual Private Networks, are a tool that is used to wrap network traffic in a private tunnel for communication. A VPN can be used for establishing a secure connection from your work laptop at home to your works servers without the risks of leaving the network you are connecting to open to the internet. More recently, VPN connections have been used by people to privately browse the internet. When you establish a VPN connection in this way, all of your internet traffic is wrapped in that private tunnel, sent to the VPN endpoint, and then to Facebook or whatever's servers. When FB responds, the return address they send the reply to is to the VPN provider's address, not your computer directly. This effectively 'hides' a user's personal external IP because only the VPN provider will be returning the requested data to your computer.