Start and Due dates can be used if you want to have a set timeframe on a task. You can also only use Start or only Due if you want to let people know when to commence a task or when a deadline is.
You can either type out the dates you want to appear on your card or you can click the field and a calendar will appear as seen above.
These dates will appear on your card and you can also track these cards in the Calendar. The calendar can also be integrated with your Google Calendar, to find out more click here.