King's Men was a name used to describe those folk of Númenor who continued to follow the counsels and teachings of the Kings of Númenor during its darkening.

Even after the kings began to turn away from the Eldar and the Valar, these Men continued to follow them, even accepting Sauron into their counsels. They persecuted and killed the Faithful and they began to worship Melkor in a temple built in their once fair city of Armenelos.

It was the King's Men who accompanied Ar-Pharazôn on his journey to conquer the land of the Valar, leaving their wives and children behind. Those who stepped foot on the shores of Aman were trapped in the Caves of the Forgotten, and the ones who remained aboard their ships were swallowed by the sea.
Encyclopedia entry originally written by Nienna-of-the-Valar