If Script is the heart of CP's interactivity, ROUTEs are the blood vessels. ROUTEs allow you to set up one-way connections between different parts of a VRML file. In this case, we're connecting the "isActive" event from the TouchSensor to the "clicked" eventIn in the Script node. The TouchSensor sends an "isActive" event whenever the user clicks down (or up) on the mouse on the TouchSensor. With this ROUTE in place, this means that the "clicked" method of the Java program will be called whenever the user clicks on the TouchSensor.
ROUTEs provide the basic infrastructure of the interactivity in your program. Don't be messy with your code or you'll end up with spaghetti ROUTEs! (Happens to me all the time.)