Why do I keep getting this warning saying "this site isn't secure" and should I be worried?

Websites use a thing called the "Hypertext Transfer Protocol" which is where the HTTP at the start of addresses comes from. 

This protocol is a standard where the two computers (or phones or whatever) send each other messages about which document to display in your browser. Things like "GET /index" (1) and "GET /tower-bridge.jpg" (2).

And those messages a…