keh₂d-tro-
“fortified place, castle”castle, castra, Chester
Instrumental giving Latin castra, English castle, Chester, -caster, -cester.
Discussion
The PIE form *keh₂d-tro- (fortified place, encampment) derives from the root *keh₂d- (to fall, to drop — extended to "to throw down, to lay"), with the instrumental suffix *-tro- producing a noun of place. The meaning is "the thing laid down" or "the place established" — a camp, a fortification, a settlement defined by its deliberate construction.
Latin castra (military camp, fortification — always plural in the military sense) is the central reflex and one of the most geographically productive words in the former Roman Empire. Every English place name ending in -caster, -cester, or -chester descends from Latin castra: Lancaster, Gloucester, Winchester, Manchester, Chester, Colchester, Doncaster, Leicester. The pattern is so regular that the suffix alone tells you a Roman fort once stood there. The word also produced castle (via Old North French castel, from Latin castellum, diminutive of castra) and the Spanish alcázar (from Arabic al-qaṣr, itself borrowed from Latin castrum).
The semantic chain from "falling/laying" to "fortification" passes through "encampment" — a camp is a place where things are laid down, where tents and ramparts are established. The Roman castra was a standardised fortified camp, built to an identical plan wherever the legions marched: rectangular, ditched, walled, with four gates aligned to the compass points. This architectural uniformity ensured that a soldier transferred from Britain to Syria would recognise the layout of his new camp — and it embedded the word castra into the geography of every province.
The related Latin noun casa (hut, cottage) may derive from the same root through a different formation, though this is debated. If connected, the semantic range extends from humble dwelling (casa → Italian/Spanish casa, "house") to military fortress (castra → castle) — two poles of architectural ambition sharing a common root.
The derivative chessboard term castling (the king's move to safety behind the rook) preserves the fortification metaphor in miniature: the king retreats into his castle.