a military encampment: the guarded quarters where an armed force is housed, and by extension the force camped there
The word begins with soldiers. In older Greek it named an army drawn up in ranks, and then the place where such an army settled: the tents, the ditch and bank thrown up around them, the whole guarded space where fighting men lived together. Everything it means in the New Testament grows out of that one picture.
Luke uses it in the plainest way, for the Roman garrison in Jerusalem. A mob seizes Paul in the temple courts and the soldiers carry him up into their quarters, a fortified block beside the temple that served as headquarters, barracks and holding cell at once. Five more times in the chapters that follow, men go up into it or come back to it, and the troops who do the fetching (στράτευμα) are named separately from the building they belong to.
Long before that, the Greek Old Testament had stretched the word in another direction, using it steadily for Israel's camp in the wilderness (מַחֲנֶה), the whole nation pitched in order around the tent of God's presence. Hebrews leans on that older usage: the bodies of the sin offerings were burned outside the camp, Jesus suffered outside the city gate, and the readers are told to go out to him there and carry the shame with him. Revelation holds the same picture at the end of the story, when the nations close in around the camp of God's people.
Once, in Hebrews 11:34, the word swings back to its oldest use and means the enemy forces themselves, the armies that Israel's champions turned back. English has to reach for three different words, "barracks", "camp" and "armies", where Greek uses one, and the thread joining them, an armed body encamped, disappears along the way.