A specimen shows how your mark is used in commerce. Acceptable specimens differ for goods and for services. For goods, an acceptable specimen could be a product label, tag, product packaging or point of sale display showing the mark where the goods can be purchased (such as on a website that has an add to cart button to purchase the product. For services, an an acceptable specimen could be an advertisement, brochure, website printout or other promotional material showing your trademark being used to identify the services.
A refusal or rejection based on an inappropriate specimen filed in connection with a trademark application or maintenance filing can arise from a number of different issues. Sometimes the trademark examiner simply needs a website URL and date accessed to appear on a specimen, other times a specimen may actually show a mark as used for goods when the application or registration covers services (or vice versa).
For more information about how to select a proper specimen, see: USPTO Specimen Guide