Most of a trademark application is description: your name, your goods, your dates. The specimen is the one part that has to be evidence. It is a picture of the mark doing its job in the real world, and it is where applications that looked straightforward suddenly stall.
What the rule requires
For goods, the regulation behind TMEP section 904.03 is specific about where the mark has to appear:
"A trademark specimen must show use of the mark on the goods, on containers or packaging for the goods, on labels or tags affixed to the goods, or on a display associated with the goods."
Those are the four places, and the list is not decorative. A photograph of the product with the name on it, a shot of the box, a label on the bottle, or a point-of-sale display: those are what the office is looking for.
Advertising is not a specimen for goods
This is the trap. The manual states that advertising material is generally not acceptable as a specimen for goods, and explains the reasoning in one sentence:
"Any material whose function is merely to tell the prospective purchaser about the goods, or to promote the sale of the goods, is unacceptable to support trademark use."
A brochure, a magazine ad, an informational insert, a page describing how good the product is: all of these tell somebody about the goods rather than being part of the goods or their sale. For services the position is different, because a service has no packaging to label, so advertising can work there.
The web page question
Almost everyone selling online asks whether a screenshot of the product page will do. It can, but not automatically. A web page qualifies when it functions as a display associated with the goods, which means it works at the point of sale rather than merely describing the product. In practice the page needs to show the mark together with the goods and give the customer a way to actually buy: a price, an order or add-to-cart control, that sort of thing.
Two mechanical requirements catch people out. A web page specimen normally has to include the URL and the date it was accessed or printed, and a cropped screenshot without them is refused on a technicality that costs weeks. The manual does allow an exception where the printout itself shows the mark on the goods or packaging in a way that would be acceptable on its own, but it is not worth relying on: adding the URL and date costs nothing.
Mockups are refused
The rules exclude artists' renderings, printer's proofs, computer illustrations, digital images and similar mockups showing how a mark may be displayed. A label composited onto a product photo in image software is exactly this, and it is refused. The specimen has to show real use, which means the product has to exist and the mark has to be on it.
This is the honest reason so many applications are filed as intent-to-use. If the product is not made yet, you cannot produce a specimen yet, and filing with a mockup does not solve that. It buys a refusal instead.
Photograph it properly
A reproduction is acceptable, including a photocopy, photograph or web page printout, as long as it shows enough of the specimen that the nature of the specimen, the mark and the goods are all identifiable. In plain terms: do not crop so tightly that only the logo is visible. The examiner has to be able to see what it is on.
Where this fits
Specimens are about proving use, which is a different question from whether you can have the name at all. That one turns on whether somebody already holds a similar mark for related goods, and no specimen fixes it. Checking whether a name is taken comes first, and the grounds of refusal cover what an examiner looks at beyond your evidence of use.
One overlap is worth flagging. On clothing, a specimen showing the name printed large across the front of a shirt can draw an ornamental refusal, because it reads as decoration rather than as a brand. A neck label photograph usually does better on both counts at once.