[svandamme]

why would you need to block "your IP", unless you are doing something illegal that might warrant somebody from investigating "who is behind the IP they found while investigating the crime"?

Your IP is justa number, an adress, and only your ISP would know who is behind that.

You could use a VPN tunnel to make it appear you are accessing the internet from another location, for instance to bypass GEO blocking by certain content providers.. but that's a whole different story.