IMPORTANT: This article only applies to the original "Treat Subtasks as Dependents" option, which has now been deprecated. For handling of subtasks in new Auto-Adjust Workflows, the "Apply this workflow to" option is now available; for details, see Including subtasks in your workflows.
Normally, the Auto-Adjust workflow type shifts dependent tasks; that is, when you change the Due Date of a task, the Start and Due Dates of all of its dependents are shifted by the same amount of time.
In addition, when you put a project under this type of workflow control, you have the option of choosing "Treat Subtasks as Dependent Tasks". If you enable (i.e. check) that option, then the above rule also applies to subtasks; i.e. if you change the Due Date of a task in the project, and that task has subtasks, then the Start and Due Dates of all of those subtasks will be shifted the same number of days that you moved their parent task.