a detestable thing: something felt as revolting, above all an idol or the equipment of pagan worship that God loathes
This is a word of strong disgust. It names a thing that turns the stomach, and in the Hebrew Bible that thing is almost always an idol. Foreign gods, carved images, and the whole apparatus of pagan worship are branded with it, so that a false god is not merely called wrong but is named as something filthy and repellent. When Solomon follows Milcom, or Josiah clears out the shrines, the objects involved are tagged with this word to say plainly what God thinks of them.
The disgust is the constant; only the target shifts. Most often the target is an idol or idolatrous object. A handful of times the word reaches past idols to name any loathsome thing: refuse hurled at a city as a public shaming, or unclean food pulled from between someone's teeth. And in the book of Daniel it settles onto one dreaded thing, a pagan object set up inside the temple itself, in a fixed phrase later readers came to call the abomination that makes desolate.
Because the word carries revulsion rather than a neutral label, translations reach for several English words to catch it: abomination, detestable thing, idol, filth. No single English word holds both the specific reference to idols and the note of loathing at once.