The phrase "to stop on" means to pause, rest or halt at a particular place. It can be used in various contexts such as stopping for food while traveling, stopping at a gas station to refuel, stopping at a hotel to spend the night, etc. The phrase is often used when referring to transportation like cars, buses, trains, and planes. For example, "We will stop on our way home to get some groceries" or "The train stopped on platform 4 for passengers to board."