What is Ember Days?

Legal Definition
In the liturgical calendar of the Western Christian churches, Ember days are four separate sets of three days within the same week — specifically, the Wednesday, Friday, and Saturday — roughly equidistant in the circuit of the year, that are set aside for fasting and prayer. These days set apart for special prayer and fasting were considered especially suitable for the ordination of clergy. The Ember Days are known in Latin as the quattuor anni tempora (the "four seasons of the year"), or formerly as the jejunia quattuor temporum ("fasts of the four seasons").

The four quarterly periods during which the ember days fall are called the embertides.
-- Wikipedia
Legal Definition
In ecclesiastical law. Those days which the ancient fathers called "quatuor tempora jejunii" are of great antiquity in the church. They are observed on Wednesday, Friday, and Saturday next after Quadragesima Sunday or the first Sunday in Lent, after Whitsuntide, Holyrood Day, in September, and St. Lucy's Day, about the middle of December. Brit c. 53. Our almanacs call the weeks in which they fall the "Ember Weeks," and they are now chiefly noticed on account of the ordination of priests and deacons; because the canon appoints the Sundays next after the Ember weeks for the solemn times of ordination, though the bishops, if they please, may ordain on any Sunday or holiday. Enc. Lond.
-- Black's Law Dictionary