When I learned driving in The Netherlands (in a car with a manual gearbox), I learned that on a down slope¹, I should switch to low gear and use the engine to brake, thus reducing the wear on the brakes. In Dutch, this is called op de motor remmen, which literally translates as braking on the engine.
In the USA, I have seen signs prohibiting engine braking:

"No engine braking" sign outside Portage, Wisconsin. Source: Wikimedia Commons.
What exactly is prohibited here, and why?
¹In The Netherlands — strictly theoretical ;-)