The Holy Innocents are the children mentioned in St. Matthew, ii, 16-18:
"Herod perceiving that he was deluded by the wise men, was exceeding angry; and sending killed all the men children that were in Bethlehem, and in all the borders thereof, from two years old and under, according to the time which he had diligently inquired of the wise men. Then was fulfilled that which was spoken by Jeremias the prophet, saying: A voice in Rama was heard, lamentation and great mourning; Rachel bewailing her children, and would not be comforted, because they are not."
Joseph, of course, had taken Mary and Jesus on the Flight Into Egypt, where they remained for some time, after an angel appeared to Joseph in a dream and warned him. The wise men, or Magi, deliberately took another route out of the country, not going back to tell Herod where they found the newborn King, but Herod was suspicious enough to just decide to kill all the Jewish boys from newborn to the age of two years.
No one knows how many children were killed in Bethlehem at Hord's command. In the Middle Ages, it was estimated to be as many as 144,000, in 1908, it was lowballed at 6 or 8, Bethlehem having been, after all, a rather small town.
The Catholic Encyclopedia, with bold text added by me, explains how St. Stephen, St. John, and the Holy Innocents relate to one another as symbols of the types of martyrs, and thus their feasts are held together, right after we celebrate the birth of Jesus. (St. Stephen -- Dec. 26, St. John -- Dec. 27, Holy Innocents -- Dec. 28.)
"The Latin Church instituted the feast of the Holy Innocents at a date now unknown, not before the end of the fourth and not later than the end of the fifth century. It is, with the feasts of St. Stephen and St. John, first found in the Leonine Sacramentary, dating from about 485. To the Philocalian Calendar of 354 it is unknown. The Latins keep it on 28 December, the Greeks on 29 December, the Syrians and Chaldeans on 27 December.
These dates have nothing to do with the chronological order of the event; the feast is kept within the octave of Christmas because the Holy Innocents gave their life for the newborn Saviour. Stephen the first martyr (martyr by will, love, and blood), John, the Disciple of Love (martyr by will and love), and these first flowers of the Church (martyrs by blood alone) accompany the Holy Child Jesus entering this world on Christmas day. Only the Church of Rome applies the word Innocentes to these children; in other Latin countries they are called simply Infantes and the feast had the title "Allisio infantium" (Brev. Goth.), "Natale infantum", or "Necatio infantum". The Armenians keep it on Monday after the Second Sunday after Pentecost (Armen. Menology, 11 May), because they believe the Holy Innocents were killed fifteen weeks after the birth of Christ."
More at:
http://www.newadvent.org/cathen/07419a.htm