When's an Ember Day is easier to answer. This coming Wednesday, Friday, and Saturday are Ember Days. On these days Western Christians traditionally fasted (ate only one meal, no earlier than midday, and 1/4 of a meal at night) and abstained from all meat products and from wine.
The Christian Cyclopedia observes:
Four periods, of 3 ember days each, set aside for fasting, prayer, and almsgiving in the 4 seasons (Lat. ieiunia [“fasts”] quatuor temporum). The pattern followed in modern times was est. in the 11th c.: Wednesday, Friday, and Saturday after (1) 1st Sunday in Lent; (2) Pentecost; (3) Holy Cross Day, September 14; (4) St. Lucia's Day, December 13.
In the Reformation times, these days were especially devoted to preaching on the Catechism. Although connected with the natural seasons and seeking God's blessings upon the fruits of the earth and acknowledging that all food comes from him, the Church thought of the words of our Lord: "the harvest is plentiful but the laborers are few." In the medieval Western Church, therefore, these days were set aside as times for the ordination - to dispatch men into the office of the ministry that through preaching the Gospel and administering the Sacraments, God might gather His harvest from the children of Adam.
For those who use The Brotherhood Prayer Book, the Ember days are provided with the following readings and collects:
Wednesday: Matthew 12:38-50 / 1 Kings 19:3-8
We beseech Thee, O Lord: that Thou wouldst graciously hear our prayers, and stretch for the right hand of Thy majesty to be our defence against all adversities; through Jesus Christ...
Friday: John 5:1-15 / Ezekiel 18:20-28
We beseech Thee, O Lord: mercifully to have compassion on Thy people, that they, which by Thee are enabled to serve Thee, may be comforted by Thy gracious and ready help; through Jesus Christ...
Saturday: Matthew 17:1-9 / 1 Thes 5:14-23
We beseech Thee, O Lord: Graciously to hear the prayers of Thy people and of Thy great goodness turn aside from them the scourges of Thine anger; through Jesus Christ...