The red "Unpublished Tasks" next to a Program name means the Program has one or multiple tasks that have been marked as unpublished.
Press the Tasks button to see which tasks are unpublished.
Here we can see the tasks within the Employee Induction Program. The flag on the Company policy says "unpublished" meaning this acknowledgement has not been published. Unpublished tasks do not prevent the Program from being assigned to and completed by users, but the unpublished task will not appear to users for completion until it has been published.