It had something to do with hunting down some fugitive or something, a woman in red (how classy) who ran around the world, and how it was up to a bunch of game show contestant kids to follow the clues and tips pouring into the Acme headquarters to track her down. Why she was so important to have a whole branch of the FBI looking for her, and why the guy always lost his mind in the "lightning round," and why the kids were called "gumshoes," and why the "Chief" only spoke in bad puns, and why the random singing, I'll never know, along with many other puzzling things about the show.
There was a lot of Dick Tracey noir-lite stuff in it, and questions about geography, but I was little and my mind was more focused on the flashing lights and other key-jingling peripherals. My favorite segment was the map race, where a lucky contestant got to try to beat the clock sticking flashing light traffic pole things to the right countries on a giant floor map of a continent. And as much as I wanted them all flashing and "wooping," I always thought that "uh oh" fart sound for a wrong pick was funnier. I wanted a couple of those flashing lights just to use around the house so I could mark my territory.
It was just something you watch as a kid when "Rockapella" actually sounds cool and you don't know any better. She always got away.