VPN is short for Virtual Private Network. This network functions as a protected network connection mostly used in public places but also of interest for companies and private users. When you surf through a VPN network you are in essence encrypting your traffic. Your online identity becomes encrypted and it is very difficult to trace your activity back to your original IP.
VPN is used to make it harder for third parties to see what you do and to collect information about your activities. It can also be a way to unlock geo-locks that restrict usage to certain countries. Some people use VPN China when they travel to this part of the world to simply be able to use their smartphones and apps as usual.
It is legal to use VPN but you need to learn more about the different services and what they cover before you choose. You can even find free VPN that works excellent for your needs.