In ancient times, under the name of “the Exaltation,” the finding of the Holy Cross was celebrated on September 14th in the West, as is still done in the East. But when in the Eighth Century the feast of May 3rd was instituted, that of September 14th was retained as one of thanksgiving for the recovery, a hundred years earlier, by the Great Emperor Heraclius, of the inestimable relic, from the infidel Chosroes, King of Persia, who had possessed himself the holy relic when pillaging the city and churches of Jerusalem. In the East the finding of the Holy Cross by St. Helena, the mother of Constantine, was celebrated with great splendor. Particles of the true Cross, were in time, brought from Jerusalem to many other churches in the East and in the West. These churches sought to imitate the solemn ceremonies in use at Jerusalem in order to do homage to the Holy Cross, the triumphant standard of our salvation.

(Source: The New Roman Missal, Rev. F. X. Lasance)