Xero private keys are used if you are connecting your own  inhouse computer to Xero.

To do this you will need a certificate file. You can use a tool such as puttygen to create a "cer" file.

Log into Xero then go to https://app.xero.com/Application

Choose New App.

Create a Private app.

You will then be presented with the consumer key and secret for private connection

Enter the Consumer Key and Consumer Token into our login screen.

Enter the path to the local key file such as “c:\XeroKeys\public_privatekey.pfx”

So upload public key to Xero, then use private_public.pfx in The Order Exchange.