Is it like a catcher giving signs to the pitcher, short-form information that means long-form stuff? A kind of compression?

Not so much on the data itself. The way serialized variables save us... One way of updating the state of entities in a game over the network is to periodically, every so often, just send the state over to all the clients. And that can be inefficient because you're sending the same values over and over again and nothing's changed. So serialized variables track when something has changed and go, okay, this one now needs to be sent. These ones that haven't changed don't need to be sent. So that saves us a lot of bandwidth.