late 13c., "unfurl" (a banner, etc.), from Old French desploiir (Modern French déployer) "unfold, unfasten, spread out" (of knots, sealed letters, etc.), from Latin displicare "to scatter," from dis- "un-, apart" (see dis-) + plicare "to fold" (see ply (v.1)).
Properly of sails or flags (and unconnected to play); meaning "reveal, exhibit" is late 14c. Related: Displayed; displaying.