When the USPTO requests that your specimen "show a connection between the trademark and the applied-for goods or services," it asks for evidence demonstrating how your trademark labels your goods/services in the marketplace. Essentially, the examiner will want proof that consumers would associate your trademark with the goods or services you are offering.
For example, if you apply for a trademark for clothing, the specimen should show the trademark on a clothing item, packaging, price tag, care tag, etc. On the other hand, if you sell fishing bait and submit a photo of your store, the USPTO would likely reject the specimen since it shows the trademark associated with a retail store, not a business producing fishing bait.
If you apply for a trademark in multiple classes, the specimens should show the association between the trademark and all your applied-for goods/services.
If you want to see this principle (and common mistakes) demonstrated in examples, visit our Specimen guide.