horn: the hard, pointed horn on an animal's head, which in Daniel's visions stands for a king and his power
The picture behind this word is plain and physical: the hard, pointed horn on an animal's head. In the night vision of Daniel 7 the fourth beast has ten of them. They are counted, watched, and then one more pushes its way up among them and shoves three of them out of the way.
A horn is an animal's weapon and the visible sign of its strength, which made it a natural picture for a ruler. Daniel's vision leaves nothing to guess at: the explanation given to the visionary says outright that the ten horns are ten kings and that another king rises after them. From there the horn in the chapter behaves like a person. It has eyes and a boasting mouth, it speaks great things, and it makes war on God's holy ones and wins for a while.
Because the chapter says what the horns stand for, a reader is not left to invent the symbolism. What Daniel does not say is which kings and which kingdoms are meant, and centuries of argument have been about that question rather than about the word.
The Hebrew word for horn (קֶרֶן) reaches much further, naming the corners of the altar, a flask of anointing oil, a hilltop, and beams of light. In the Aramaic of the Bible this word stays close to home: horns on a beast, kings, and the horn blown as an instrument.