A tropaion (Greek: τρόπαιον, Latin: tropaeum), whence English "trophy" is derived, is an ancient Greek and later Roman monument set up to commemorate a victory over one's foes. Typically this takes the shape of a tree, sometimes with a pair of arm-like branches (or, in later times, a pair of stakes set crosswise) upon which is hung the armour of a defeated and dead foe. The tropaion is then dedicated to a god in thanksgiving for the victory.
In the Greek city-states of the Archaic period, the tropaion would be set up on the battlefield itself, usually at the site of the "turning point" (Gk. tropê) at which the routed enemy's phalanx broke, turned and ran. It would be dressed in the typical hoplite of the period, including (at different times), a helmet, cuirass (either of bronze or linen), and a number of shields,etc., would be piled about the base. It remained on the battlefield until the following season's campaigns (since battles were often fought in the same, relatively few plains amid Greece's numerous mountains), where it might be replaced with a new trophy.
In later eras in the Greek world, these tropaia might be vowed at the battle-site, but in fact erected at pan-Hellenic sanctuaries such as Olympia or Delphi to further increase the prestige of the victorious state.
The significance of the monument is a ritualistic notification of "victory" to the defeated enemies. Since warfare in the Greek world was largely a ritualistic affair in the archaic hoplite-age (see Hanson, The Western Way of War for further elaboration of this idea), the monument is used to reinforce the symbolic capital of the victory in the Greek community.