Action date means the day when the remark (action) must be processed by a person in charge.
Once the action is completed, push 'Confirm' button to mark it as done.
Action date can be highlighted with a blue (in a calendar) and red (in a remark) color if it comes to a weekend or a holiday.
Those days to be defined in advance in Tools → Company Settings → Settings → General → WeekendDaysAndPublicHolidays.
For all internal remarks (Customer, Order, Invoice) it works in all the places where corresponding remarks can be viewed/edited: