Thursday is the Feast of the Triumph or Exaltation of the Holy Cross. This is not the commemoration of Our Lord’s suffering upon the Cross – that is Good Friday. Rather it is an invitation to honour the Cross itself, the altar as it were where Jesus made the ultimate sacrifice for us. There are many versions of what happened to the True Cross, here we mention the most popular tradition in Western Christianity.
“According to Christian tradition, the True Cross was discovered in 326 by Saint Helena, the mother of the Roman Emperor Constantine the Great, during a pilgrimage she made to Jerusalem. The great Church of the Holy Sepulchre was then built at the site of the discovery, by order of Helena and Constantine. The church was dedicated nine years later, with a portion of the cross. One-third remained in Jerusalem, one-third was brought to Rome and deposited in the church of Santa Croce in Gerusalemme (Holy Cross in Jerusalem), also known as the Sessorian basilica, and one-third was taken to Constantinople to make the city impregnable. (https://en.wikipedia.org/wiki/Feast_of_the_Cross)
14th September, the date of the feast, marks the dedication of the Church of the Holy Sepulchre in 335. This was a two-day festival: although the actual consecration of the church was on 13 September, the cross itself was brought outside the church on 14 September so that the clergy and faithful could pray before the True Cross, and all could come forward to venerate it.
Historically in Western Christianity, the Wednesday, Friday, and Saturday of the calendar week after the one in which the feast day occurs are designated as one of each year’s four sets of Ember days. Until 1969, these ember days were a part of the liturgical calendar of the Roman Catholic Church. Organization of these celebrations in the ordinary form is now left to the decision of episcopal conferences in view of local conditions and customs. The ember days are no longer part of our Latin Rite, but are still observed in the calendar of the Roman Rite’s Extraordinary Form, the Anglican Ordinariate, and Western Orthodoxy.”
Fr Matthew, with acknowledgements to Wikipedia.