Note, while most Missals call for Ember Wednesday and Ember Saturday to be a day of partial abstinence, this is a rather modern practice. Partial Abstinence refers to eating meat only at the principal meal of the day and do not permit meat to be eaten as part of the collation or the frustulum. Partial abstinence started only in 1741 under Pope Benedict XIV as a concession & as part of a gradual decline of fasting. It is better to keep all Ember Days as days of complete abstinence. Ember Fridays of course are in all Missals days of complete abstinence.
From Angelus Press Daily Missal:
At the beginning of the four seasons of the Ecclesiastical Year, the Ember Days have been instituted by the Church to thank God for blessings obtained during the past year and to implore further graces for the new season. Their importance in the Church was formerly very great. They are fixed on the Wednesday, Friday, and Saturday: after the First Sunday of Lent for spring, after Pentecost Sunday for summer, after the Feast of the Exaltation of the Cross (14th September) for autumn, and after the Third Sunday of Advent for winter. They are intended, too, to consecrate to God the various seasons in nature, and to prepare by penance those who are about to be ordained. Ordinations generally take place on the Ember Days. The faithful ought to pray on these days for good priests. The Ember Days were until c. 1960 fastdays of obligation.
To-day the Church begins the fast of Quatuor Tempora, or, as we call it, of Ember days: it includes also the Friday and Saturday of this same week. This observance is not peculiar to the Advent liturgy; it is one which has been fixed for each of the four seasons of the ecclesiastical year. We may consider it as one of those practices which the Church took from the Synagogue; for the prophet Zacharias speaks of the fasts of the fourth, fifth, seventh, and tenth months.[1] Its introduction into the Christian Church would seem to have been made in the apostolic times; such, at least, is the opinion of St. Leo, of St. Isidore of Seville, of Rabanus Maurus, and of several other ancient Christian writers. It is remarkable, on the other hand, that the orientals do not observe this fast.
From the first ages the Quatuor Tempora were kept, in the Roman Church, at the same time of the year as at present. As to the expression, which is not unfrequently used in the early writers, of the three times and not the four, we must remember that in the spring, these days always come in the first week of Lent, a period already consecrated to the most rigorous fasting and abstinence, and that consequently they could add nothing to the penitential exercises of that portion of the year.
The intentions, which the Church has in the fast of the Ember days, are the same as those of the Synagogue; namely, to consecrate to God by penance the four seasons of the year. The Ember days of Advent are known, in ecclesiastical antiquity, as the fast of the tenth month; and St. Leo, in one of his sermons on this fast, of which the Church has inserted a passage in the second nocturn of the third Sunday of Advent, tells us that a special fast was fixed for this time of the year, because the fruits of the earth had then all been gathered in, and that it behoved Christians to testify their gratitude to God by a sacrifice of abstinence, thus rendering themselves more worthy to approach to God, the more they were detached from the love of created things. 'For fasting,’ adds the holy doctor, 'has ever been the nourishment of virtue. Abstinence is the source of chaste thoughts, of wise resolutions, and of salutary counsel. By voluntary mortifications, the flesh dies to its concupiscences, and the spirit is renewed in virtue. But since fasting alone is not sufficient whereby to secure the soul’s salvation, let us add to it works of mercy towards the poor. Let us make that which we retrench from indulgence, serve unto the exercise of virtue. Let the abstinence of him that fasts, become the meal of the poor man.’
Let us, the children of the Church, practise what is in our power of these admonitions; and since the actual discipline of Advent is so very mild, let us be so much the more fervent in fulfilling the precept of the fast of the Ember days. By these few exercises which are now required of us, let us keep up within ourselves the zeal of our forefathers for this holy season of Advent. We must never forget that although the interior preparation is what is absolutely essential for our profiting by the coming of our Lord Jesus Christ, yet this preparation could scarcely be real unless it manifested itself by the exterior practices of religion and penance.
The fast of the Ember days has another object besides that of consecrating the four seasons of the year to God by an act of penance: it has also in view the ordination of the ministers of the Church, which
takes place on the Saturday, and of which notice was formerly given to the people during the Mass of the Wednesday. In the Roman Church, the ordination held in the month of December was, for a long time, the most solemn of all; and it would appear, from the ancient chronicles of the Popes, that, excepting very extraordinary cases, the tenth month was, for several ages, the only time for conferring Holy Orders in Rome. The faithful should unite with the Church in this her intention, and offer to God their fasting and abstinence for the purpose of obtaining worthy ministers of the word and of the Sacraments, and true pastors of the people.
From New Advent:
Ember days (corruption from Lat. Quatuor Tempora, four times) are the days at the beginning of the seasons ordered by the Church as days of fast and abstinence. They were definitely arranged and prescribed for the entire Church by Pope Gregory VII (1073-1085) for the Wednesday, Friday, and Saturday after 13 December (S. Lucia), after Ash Wednesday, after Whitsunday, and after 14 September (Exaltation of the Cross). The purpose of their introduction, besides the general one intended by all prayer and fasting, was to thank God for the gifts of nature, to teach men to make use of them in moderation, and to assist the needy. The immediate occasion was the practice of the heathens of Rome. The Romans were originally given to agriculture, and their native gods belonged to the same class.
At the beginning of the time for seeding and harvesting religious ceremonies were performed to implore the help of their deities: in June for a bountiful harvest, in September for a rich vintage, and in December for the seeding; hence their feriae sementivae, feriae messis, and feri vindimiales. The Church, when converting heathen nations, has always tried to sanctify any practices which could be utilized for a good purpose. At first the Church in Rome had fasts in June, September, and December; the exact days were not fixed but were announced by the priests. The "Liber Pontificalis" ascribes to Pope Callistus (217-222) a law ordering: the fast, but probably it is older. Leo the Great (440-461) considers it an Apostolic institution. When the fourth season was added cannot be ascertained, but Gelasius (492-496) speaks of all four. This pope also permitted the conferring of priesthood and deaconship on the Saturdays of ember week--these were formerly given only at Easter.
Before Gelasius the ember days were known only in Rome, but after his time their observance spread. They were brought into England by St. Augustine; into Gaul and Germany by the Carlovingians. Spain adopted them with the Roman Liturgy in the eleventh century. They were introduced by St. Charles Borromeo into Milan. The Eastern Church does not know them. The present Roman Missal, in the formulary for the Ember days, retains in part the old practice of lessons from Scripture in addition to the ordinary two: for the Wednesdays three, for the Saturdays six, and seven for the Saturday in December. Some of these lessons contain promises of a bountiful harvest for those that serve God.
From Catholic Culture:
Since man is both a spiritual and physical being, the Church provides for the needs of man in his everyday life. The Church's liturgy and feasts in many areas reflect the four seasons of the year (spring, summer, fall and winter). The months of August, September, October and November are part of the harvest season, and as Christians we recall God's constant protection over his people and give thanksgiving for the year's harvest.
The September Ember Days were particularly focused on the end of the harvest season and thanksgiving to God for the season. Ember Days were three days (Wednesday, Friday and Saturday) set aside by the Church for prayer, fasting and almsgiving at the beginning of each of the four seasons of the year. The ember days fell after December 13, the feast of St. Lucy (winter), after the First Sunday of Lent (spring), after Pentecost Sunday (summer), and after September 14 , the feast of the Exaltation of the Holy Cross (fall). These weeks are known as the quattor tempora, the "four seasons."
Since the late 5th century, the Ember Days were also the preferred dates for ordination of priests. So during these times the Church had a threefold focus: (1) sanctifying each new season by turning to God through prayer, fasting and almsgiving; (2) giving thanks to God for the various harvests of each season; and (3) praying for the newly ordained and for future vocations to the priesthood and religious life.