The feast day honors the innocent children martyred by Herod the Great when he ordered the execution of all male children up to the age of two years old in the vicinity of the town of Bethlehem. The Catholic Church regards these innocent children as the very first Christian martyrs. This massacre is told in the Gospel of Matthew, chapter 2, when the three Magi visited Jerusalem searching for the newborn King. Herod gathers his priests and scribes together, demanding where the child would be born - he was told Bethlehem as the prophets had written.
Herod sends the Magi out, asking them to return when they find him. They do find Christ, with Mary and his mother and after presenting gifts, they are warned in a dream not to return to Herod. In verse 16-18:
16 Then Herod, when he saw that he was mocked of the wise men, was exceeding wroth, and sent forth, and slew all the children that were in Bethlehem, and in all the coasts thereof, from two years old and under, according to the time which he had diligently inquired of the wise men.
17 Then was fulfilled that which was spoken by Jeremiah the prophet, saying,
18 In Rama was there a voice heard, lamentation, and weeping, and great mourning, Rachel weeping for her children, and would not be comforted, because they are not.
The commemoration of this terrible massacre first appears as a feast in the Leonine Sacramentary dating around the year 485 AD. Saint Leo spoke of the Innocents and Fulgentius of Ruspe (6th century AD) gave a homily recorded as De Epiphania, deque Innocentum nece et muneribus magorum ("On Epiphany, and on the murder of the Innocents and the gifts of the Magi").
Today the feast is held on the fourth day of Christmastide (28th of December) in the Catholic Church, the 27th of December for West Syrians, January 10th for East Syrians, and December 29th for the Eastern Orthodox Church.