The procession on this day is in no way related to the feast of St. Mark; if the feast be transferred the Great Litanies are not transferred, unless Easter Sunday should fall on April 25, when the procession would take place on the following Tuesday. The feast of St. Mark was not regularly inserted into the Roman Calendar until about the Twelfth Century. This is explained by the original association of the commemorations of the saints with their tombs. Although St. Mark was among the first who with St. Peter brought the Faith to Rome and at the request of the Romans themselves, wrote his Gospel, he did not die in the Holy City.
Mark is said to have been the young man who, on the night that Jesus was made prisoner, left the sheet in which he was clothed, in the hands of the soldiers and fled naked. He accompanied his cousin Barnabas and Paul, on their first apostolic mission. Paul, however, would not take him along on the second journey; when Paul was in prison at Rome, Mark again was closely associated with him. To St. Mark is attributed the foundation of the Church in Alexandria, which See he governed for about twenty years and in the end was martyred, about the year 70. His body was taken to Venice whose patron he has been since the Ninth Century and where there is a great Basilica dedicated to his name.
(Source: Fr. Lasance, The New Roman Missal)