It's to show that your seat is reserved between those stops.

Previously these seats would.have had little ticket things put into a slot on the top of the seat.

Are these not standard though? Do American trains not have these? How are reserved seats identified without them?

Thats your reservation, so other passengers can see that they can use the seat before they arrive at Amsterdam and after Köln

IC/ICE, the german highspeed trains. It shows what seats are reserved between what stations. This way if the train starts in Cologne over Frankfurt to Munich, and a seat is reserved between Frankfurt and Munich you can sit down there between Cologne and Frankfurt but have to give up the seat to the person who reserved it

These seats are reserved in-between Cologne and Amsterdam.

It is to avoid to conflicts about the seating

Maybe they have fixed seats, like in Japan.

In many countries, you don't put in a reservation for a seat separately

Great system until "Wir haben leider ein Problem mit den Reservierungsanzeigen an Bord. " Quite common unfortunately.

Only international trains in the Netherlands have the option to reserve seats at all. Regular train seats work on a "too bad, so sad" basis with seats.

Though in all my years in traveling by train i maybe didnt have a seat twice during rush hour