Becky -
As Sheri indicated, this flag prevents the User Story from changing state when the state of a child Task is updated. There is a full description of this in the help here:
https://help.rallydev.com/task-state-updates-parent-schedule-state
Many Kanban Teams like to disable these auto-state changes because having state unintentionally move forward/backward causes inconsistencies with their flow-based (i.e., Time in State) metrics. We also see teams that use the same User Story for development and deployment disable the auto-state changes. In this case, all of the development tasks are created and Completed first, which causes the Story to be marked Completed. Later, the deployment Tasks are added to the Story, which causes the state to move back to In Progress (since not all Tasks are completed anymore). These teams would rather do the Story state changes manually so they can choose when the Story is considered "Complete" for their metrics -- when development is done or when deployment is done.