If someone, especially a police officer, tells you to move along, or if they move you along, they tell you to stop standing in a particular place and to go somewhere else. Curious pedestrians were ordered to move along Our officers are moving them along and not allowing them to gather in large groups
If a process moves along or if something moves it along, it progresses. Research tends to move along at a slow but orderly pace Delay is part of the normal process, but I hope we can move things along