Fields may be added to orders. The purpose of fields on orders is to allow administrators to track extra information about an order. There are no instructions for printing fields on orders for this reason.
What You Can Do with Order Fields
This feature is best used with the Chrome plugin to allow you to update all order information from within the Shopify interface. Examples of admin use for this field include order notes, order pictures (admin only), etc.
Exporting Order Data
Custom Fields can export all order data to a spreadsheet by using the Bulk Export feature. In order to do this, just hover over the orders tab and click on Export like shown below.
From this screen, you can export Additional Columns such as Email, Paid at (specific paid time data), and Financial Status. If you don't have Custom Fields on any orders you can also use the check-box for Including orders that don't have Custom Fields.
By dropping down the Export Filters menu, you can filter certain orders. This is useful if you only want orders from last year or the last few months, etc.
Additional Resources & Information
Custom Fields: Working with Emails - This article goes in depth about showing field data in an order email.
Custom Fields: Bulk Operations Section - This section goes in depth with the import/export operations in Custom Fields.