From here.

After the death and resurrection of Christ, both the Jewish and Roman authorities in Jerusalem made efforts to obscure the Holy Sepulchre, Christ’s tomb in the garden near the site of His crucifixion. The earth had been mounded up over the site, and pagan temples had been built on top of it. The Cross on which Christ had died had been hidden (tradition said) by the Jewish authorities somewhere in the vicinity.

According to tradition, first mentioned by Saint Cyril of Jerusalem in 348, Saint Helena, nearing the end of her life, decided under divine inspiration to travel to Jerusalem in 326 to excavate the Holy Sepulchre and attempt to locate the True Cross. A Jew by the name of Judas, aware of the tradition concerning the hiding of the Cross, led those excavating the Holy Sepulchre to the spot in which it was hidden.

Three crosses were found on the spot. According to one tradition, the inscription Iesus Nazarenus Rex Iudaeorum (“Jesus of Nazareth, King of the Jews”) remained attached to the True Cross. According to a more common tradition, however, the inscription was missing, and Saint Helena and Saint Macarius, the bishop of Jerusalem, assuming that one was the True Cross and the other two belonged to the thieves crucified alongside Christ, devised an experiment to determine which was the True Cross.

In one version of the latter tradition, the three crosses were taken to a woman who was near death; when she touched the True Cross, she was healed. In another, the body of a dead man was brought to the place where the three crosses were found, and laid upon each cross. The True Cross restored the dead man to life.

In celebration of the discovery of the Holy Cross, Constantine ordered the construction of churches at the site of the Holy Sepulchre and on Mount Calvary. Those churches were dedicated on September 13 and 14, 335, and shortly thereafter the Feast of the Exaltation of the Holy Cross began to be celebrated on the latter date. The feast slowly spread from Jerusalem to other churches, until, by the year 720, the celebration was universal.

In the early seventh century, the Persians conquered Jerusalem, and the Persian king Khosrau II captured the True Cross and took it back to Persia. After Khosrau’s defeat by Emperor Heraclius II, Khosrau’s own son had him assassinated in 628 and returned the True Cross to Heraclius. In 629, Heraclius, having initially taken the True Cross to Constantinople, decided to restore it to Jerusalem. Tradition says that he carried the Cross on his own back, but when he attempted to enter the church on Mount Calvary, a strange force stopped him. Patriarch Zacharias of Jerusalem, seeing the emperor struggling, advised him to take off his royal robes and crown and to dress in a penitential robe instead. As soon as Heraclius took Zacharias’ advice, he was able to carry the True Cross into the church.

For some centuries, a second feast, the Invention of the Cross, was celebrated on May 3 in the Roman and Gallican churches, following a tradition that marked that date as the day on which Saint Helena discovered the True Cross. In Jerusalem, however, the finding of the Cross was celebrated from the beginning on September 14.

During the reign of Constantine, first Roman Emperor to profess the Christian faith, his mother Helena went to Israel and there undertook to find the places especially significant to Christians. (She was helped in this by the fact that in their destructions around 135, the Romans had built pagan shrines over many of these sites.) Having located, close together, what she believed to be the sites of the Crucifixion and of the Burial (at locations that modern archaeologists think may be correct), she then had built over them the Church of the Holy Sepulchre, which was dedicated on 14 September 335. It has become a day for recognizing the Cross (in a festal atmosphere that would be inappropriate on Good Friday) as a symbol of triumph, as a sign of Christ’s victory over death, and a reminder of His promise, “And when I am lifted up, I will draw all men unto me.” (John 12:32)

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Exaltation of the Holy Cross (Roodmas)

 September 14, 335 

Roodmas¹ — more commonly known simply as “Holy Cross Day” — was first begun to commemorate the Dedication of the Basilica of the Resurrection, built by St. Helena (Constantine the Great’s mother), in Jerusalem in A.D. 335 — but the true Cross was found shortly thereafter, also by St. Helena, so the two events were joined.

The story of the finding of the True Cross, from the Catholic Encyclopedia:

In the year 326 the mother of Constantine, Helena, then about 80 years old, having journeyed to Jerusalem, undertook to rid the Holy Sepulchre of the mound of earth heaped upon and around it, and to destroy the pagan buildings that profaned its site. Some revelations which she had received gave her confidence that she would discover the Saviour’s Tomb and His Cross. The work was carried on diligently, with the co-operation of St. Macarius, bishop of the city.

The Jews had hidden the Cross in a ditch or well, and covered it over with stones, so that the faithful might not come and venerate it. Only a chosen few among the Jews knew the exact spot where it had been hidden, and one of them, named Judas, touched by Divine inspiration, pointed it out to the excavators, for which act he was highly praised by St. Helena. Judas afterwards became a Christian saint, and is honoured under the name of Cyriacus.

During the excavation three crosses were found, but because the titulus was detached from the Cross of Christ, there was no means of identifying it. Following an inspiration from on high, Macarius caused the three crosses to be carried, one after the other, to the bedside of a worthy woman who was at the point of death. The touch of the other two was of no avail; but on touching that upon which Christ had died the woman got suddenly well again.

From a letter of St. Paulinus to Severus inserted in the Breviary of Paris it would appear that St. Helena herself had sought by means of a miracle to discover which was the True Cross and that she caused a man already dead and buried to be carried to the spot, whereupon, by contact with the third cross, he came to life. From yet another tradition, related by St. Ambrose, it would seem that the titulus, or inscription, had remained fastened to the Cross.

After the happy discovery, St. Helena and Constantine erected a magnificent basilica over the Holy Sepulchre, and that is the reason why the church bore the name of St. Constantinus. The precise spot of the finding was covered by the atrium of the basilica, and there the Cross was set up in an oratory, as appears in the restoration executed by de Vogüé. When this noble basilica had been destroyed by the infidels, Arculfus, in the seventh century, enumerated four buildings upon the Holy Places around Golgotha, and one of them was the “Church of the Invention” or “of the Finding”. This church was attributed by him and by topographers of later times to Constantine. The Frankish monks of Mount Olivet, writing to Leo III, style it St. Constantinus. Perhaps the oratory built by Constantine suffered less at the hands of the Persians than the other buildings, and so could still retain the name and style of Martyrium Constantinianum. (See De Rossi, Bull. d’ arch. crist., 1865, 88.)

A portion of the True Cross remained at Jerusalem enclosed in a silver reliquary; the remainder, with the nails, must have been sent to Constantine, and it must have been this second portion that he caused to be enclosed in the statue of himself which was set on a porphyry column in the Forum at Constantinople; Socrates, the historian, relates that this statue was to make the city impregnable. One of the nails was fastened to the emperor’s helmet, and one to his horse’s bridle, bringing to pass, according to many of the Fathers, what had been written by Zacharias the Prophet: “In that day that which is upon the bridle of the horse shall be holy to the Lord” (Zechariah 14:20). Another of the nails was used later in the Iron Crown of Lombardy preserved in the treasury of the cathedral of Monza.

Scientific study of the relics of the True Cross show it to be made of some species of pine. The titulus crucis  —  the wood on which the inscription “Jesus of Nazareth, King of the Jews” was written in Latin, Greek, and Hebrew (Matthew 27:37, Mark 15:26, Luke 23:38 and John 19:19)  —  is made of an olive wood. The titulus has been scientifically dated to the 1st c. and the script is still legible (interestingly, the Latin and Greek are in reverse script), though the Hebrew is missing due to the entire thing being halved, the second half having been lost in the 6th century. It is from the Latin inscription  —  “Iesus Nazarenus Rex Iudeorum” that we get the abbreviation “I.N.R.I.” that is found on many Crucifixes.

The titulus crucis and relics of the True Cross can be seen in Rome’s Basilica di Santa Croce in Gerusalemme.

Footnote:
 ¹“Rood” is the Middle English word for “Cross.”