Reading Apel's Gregorian Chant Chapter Two about the liturgy, I came across the term Ember days. I remember hearing the term when I was a kid, but I never understood them or remember seeing them observed.
What I do know at this point is that Ember days used to be observed during one week at the start of each of the four seasons of the year. During those weeks, Wednesday, Thursday and Saturday were set aside for fasting and prayer.
Ordinations to the diaconate and the priesthood occurred on Ember Saturdays. I recently attended the ordination of my brother in Carmel, Lawrence Poncini OCD, on the Saturday after Pentecost, which is an Ember Week. So, it seems that even though the United States Conference of Catholic Bishops has downplayed Ember days, and even though their observance has just about disappeared, ordinations are still performed according to the old observance.
The Latin name for those four times was Quatuor Temporum -- which means Four Times. They occurred in Winter during Advent (after St. Lucy's feast on Dec. 13), Spring (after Ash Wednesday, between the First and Second Sundays of Lent), Summer (the week after Pentecost), and Fall (the week after the Exaltation of the Holy Cross.
The term Ember Days evolved from Quatuor Temporum as follows, according to Essays on Liturgiology and Church History by Anglican Divine, Rev. J. M. Neale, D.D.. "In French and Italian the term is the same; in Spanish and Portuguese they are simply Temporas. German converts them into Quatember, and thence, by the easy corruption of dropping the first syllable, a corruption which also takes place in some other words, we get the English Ember." From "Church Festivals and Their Household Words" in Neal Lectures of Litergiology
I found some good answers to my related question, "Whatever Happened to Ember Days?" about the post Vatican II decision to drop Ember days from the Church calendar at Benedictus Deus blog. He references a 2003 meeting of the USCCB discussing and downplaying Ember Days. Also important on this topic is the Ember Days posting at the 1938 Catholic Encyclopedia online, which ends "Some of these lessons [from the Ember Days readings from the Roman Missal] contain promises of a bountiful harvest for those that serve God."