Would like to understand the importance of special calendar while selecting invoices for payment. For e.g. if as per the payment selection criteria, a list of invoices has been selected and if we want to ensure that a few invoices should not be selected at all by the system, we can use special calendar. But i am not sure how it works?

Special Calendar could be used for various purposes:

Recurring Invoice
Withholding Tax
Payment Terms
Key Indicator

Payment terms could be created based on special calendars.
You then assign payment terms to the invoices.
That means due dates for the invoices could be based on the special calendars.
In your payment selection criteria you specify the cut off date; meaning all invoices due on or before that date are picked up.
This is how you can use special calendars in selection process.