Although I don't know precisely, I can guess that if it's a challenge that requires building something in your DE Org, Trailhead establishes a connection to that Org and access it through the API to check that the requirements are met. For example in the Apex Trigger challenge it probably checks to confirm that there is a Trigger called "AccountAddressTrigger" and then inserts an Account with Match_Billing_Address__c = TRUE and verifies that the Trigger does in fact update the appropriate postal code field that the instructions demand.
So, you MUST use the Connect to your Developer Edition button to ensure that Trailhead is connected and can check your work!
All Answers
So, you MUST use the Connect to your Developer Edition button to ensure that Trailhead is connected and can check your work!