One of the most distinguished, and familiar instances of veneration and veiling for Catholics is the veiling of crosses and holy images from Passion Sunday until Good Friday ending with the veneration of the cross. This veiling and veneration occurs in Lent, when the liturgy is celebrated with a certain emptiness. The organ is silent, as are bells, and certain prayers are not said; and the altar is not vibrantly decorated. This veiling is sometimes called the, "fasting of the eyes." However, it is not intended as a withdrawl from the senses. Rather, it comes from a long line of tradition surrounded by the authentic Cross of Christ that St. Helen found in Jerusalem.
Like most relics, the Holy Cross was wrapped up in cloths and spent its time in Rome's sacristy. On Good Friday it was brought into the church and unpacked in a solemn ritual so that it could be revealed to the faithful. Two deacons would stand on either side of it, as the faithful came up to kiss it, making sure that no one would be tempted to steal a splinter from it. Actually, different Bishops would be tempted (and are known to have been the main culprits) more than anyone to take a piece to bring back home to their territories.
Once the relic splinters were taken back to the Bishop's home territories throughout Europe, they were treated the same as the authentic cross was treated in Rome. The relics were wrapped up in cloth and brought out on Good Friday for veneration.
In the end, this ritual was adopted by communities that had no relic of the True Cross. Instead, the cross above the altar was taken down and wrapped up, to be venerated on Good Friday in the same way the Vera Crux.
The purpose of veiling and veneration was/is not to withdraw the cross from sight, but rather it was so that the cross would be treated like the True Cross; from being a devotional object, a sacred object, it would once again become the real instrument of torture (and salvation) on which Christ died.