Before we could go further, it is necessary for us to understand the meaning of “obligation” and “Holy Day”
An obligation is that duty you must do because you have promised or because you are bound by the law to do so.
A Holy Day is a day dedicated to religious observances. It is a consecrated religious festival other than Sundays. In order words, Holy Days of obligation are feast days and holidays on which Roman Catholics are duty-bound to attend Mass and avoid (to their ability) servile work on that day. Therefore, they are requested to rest from work and recreation. These observances are listed in the canon law (Canon 1246 of the 1983 code) and are part of the Sunday duty, the first of the precept of the church.
Catholics are required to engage in the primary form of worship – the Holy Mass. Currently, there are ten (10) Holy days of obligations in the Latin Rites of the Catholic Church. In the Eastern Catholic Church there are five (5) and in the United States, only six (6) days of obligation are practiced which are: the January 1 Solemnity of Mary, Thursday of the Sixth Week of Easter (the Ascension), August 15 (the Assumption), November 1 (Solemnity of the Saints), December 8 (Immaculate Conception) and December 25 (Christmas).
Here are the 10 days of obligation (apart from Sundays) the Canon mentions:
January 1: Solemnity of Mary, the Holy Mother of God.
January 6: Solemnity of the Epiphany of the Lord.
March 19: Solemnity of Saint Joseph, Spouse of the Blessed Virgin Mary.
Thursday of the Sixth Week of Eastertide (40 days after Easter): Solemnity of the Ascension of the Lord.
Thursday after Trinity Sunday: Solemnity of the Most Holy Body and Blood of Christ (Corpus Christi).
June 29: Solemnity of Saint Peter and Paul the Apostles.
August 15: Solemnity of the Assumption of the Blessed Virgin Mary.
November 1: Solemnity of all Saints.
December 8: Solemnity of the Immaculate Conception of the Blessed Virgin Mary.
December 25: Solemnity of the Nativity of the Lord (Christmas)
Before Pope Pius X reduced the Holy Days of obligation, they were much greater than ten. He reduced the number of such non-Sunday holy days from 36 to 8. The feast celebrated on January 1 was then the feast of the Circumcision of Christ. This present list was established in Canon 1247 of the 1917 code of Canon Law, now Canon 1246 of the current code of the Canon Law.
Non-Sunday holy days of obligation all have the rank of Solemnity. If in Ordinary Times one of the falls on a Sunday, the Sunday celebration gives way to it. The Sundays of Advent, Lent, and Eastertide take precedence over all solemnity, which is then transferred to another day.
Attending Mass on Sundays and Holy Days of Obligation is not an arbitrary rule but part of general moral life. That is, the need to do good and avoid evil with reference to the Catholic Catechism (Para 2041). The Church uses the Precepts of the Church (the Holy days of obligation is one of them) simply as a way to remind adherents of the need to grow in holiness.