The Thin Blue Line is a generic term for a police force. Our police, worldwide, mostly do an incredible job of keeping us safe and we should thank them more than we do.
Our police continually put themselves in danger these days just by being a cop. They are a target for terrorisism and are the first responders when a suspiscious object is found.
Their hard work catching criminals is sometimes wasted by smart criminal lawers who manage to somehow cast enough doubt upon evidence presented to have the crim set free to re-offend.
The reference “The Thin Blue Line” originates from the way the police are prepared to line up across a street in single file and face down a riotous mob of protestors who throw bricks, lumps of concrete, stones, and any other projectile they can lay their hands on at the line of police.