Flagging best customers will provide 2 benefits:

At the end of each day a Summary screen appears after the store is closed.

On this screen is a list of customers, and their total orders.

Simply tap on the star to flag the customer as a best customer.

Once Flagged, the star will become yellow.  To un-flag just press on the star once more.

A star will appear next to the customers name when an order arrives: