How did the celebration of Advent come about?

The liturgical season of Advent marks the time of spiritual preparation by the faithful before Christmas.  Advent begins on the Sunday closest to the Feast of St. Andrew the Apostle (November 30).  It spans four Sundays and four weeks of preparation, although the last week of Advent is usually truncated because of when Christmas falls.  (For instance, some years, the fourth Sunday of Advent is obviously on Sunday, and then that evening is Christmas Eve.) 
 
The celebration of Advent has evolved in the spiritual life of the Church.  The historical origins of Advent are hard to determine with great precision.  In its earliest form, beginning in France, Advent was a period of preparation for the Feast of the Epiphany, a day when converts were baptized; so the Advent preparation was very similar to Lent with an emphasis on prayer and fasting which lasted three weeks and later was expanded to 40 days.  In 380, the local Council of Saragossa, Spain, established a three-week fast before Epiphany.  Inspired by the Lenten regulations, the local Council of Macon, France, in 581 designated that from November 11 (the Feast of St. Martin of Tours) until Christmas fasting would be required on Monday, Wednesday, and Friday.  Eventually, similar practices spread to England.  In Rome, the Advent preparation did not appear until the sixth century, and was viewed as a preparation for Christmas with less of a penitential bent. 
 
The Church gradually formalized the celebration of Advent as a period of spiritual preparation for Christmas.  The Gelasian Sacramentary, traditionally attributed to Pope St. Gelasius I (d. 496), was the first to provide Advent liturgies for five Sundays.  Later, Pope St. Gregory I (d. 604) enhanced these liturgies composing prayers, antiphons, readings, and responses.  Pope St. Gregory VII (d. 1095) later reduced the number of Sundays in Advent to four.  Finally, about the ninth century, the Church designated the first Sunday of Advent as the beginning of the Church year. 
 
Despite the “sketchy” history behind Advent, the importance of this season remains to focus on the coming of our Lord.  (The word Advent comes from the Latin adventus, meaning “coming.”)  The Catechism stresses the two-fold meaning of this “coming”: “When the Church celebrates the liturgy of Advent each year, she makes present this ancient expectancy of the Messiah, for by sharing in the long preparation for the Savior’s first coming, the faithful renew their ardent desire for His second coming” (#524). 
 
Therefore, on one hand, the faithful reflect back and are encouraged to celebrate the anniversary of the Lord’s first coming into this world.  We ponder again the great mystery of the incarnation when our Lord humbled Himself, taking on our humanity, and entered our time and space to free us from sin.  On the other hand, we recall in the Creed that our Lord will come again to judge the living and the dead and that we must be ready to meet Him. 
 
In all, during Advent we strive to fulfill the opening prayer for the Mass of the First Sunday of Advent: “Father in Heaven,… increase our longing for Christ our Savior and give us the strength to grow in love, that the dawn of His coming may find us rejoicing in His presence and welcoming the light of His truth.” 

SOURCE: https://catholicstraightanswers.com/how-did-the-celebration-of-advent-come-about/