Why are some days and seasons more important for the Church?

To grow in faith and holiness, in addition to the obligatory Sunday Mass and Holy Days of Obligation, there is a richness and beauty contained in the Church’s liturgical calendar. Holy days and solemnities are a great opportunity to enrich our spiritual life!

During the course of the liturgical year, the Church celebrates the whole mystery of Christ, from His incarnation and birth to His ascension, to Pentecost and the founding of the Church, and finally to the second coming of Christ in judgment on the Solemnity of Christ the King. On Sundays in particular, we commemorate the Resurrection, when our Lord triumphed over sin and death. In a special way, the Church also honors our Blessed Mother, marking those special events of her participation in the mystery of salvation. Finally, the Church also commemorates the memorial days of saints, who through their lives bring to the minds of the faithful the call to holiness.

Technically, the divisions are as follows:
Solemnities are the celebrations of greatest importance. Each Solemnity begins on the prior evening with Vigil Mass. On these days, both the Gloria and the Creed are recited (except on Sunday’s during Lent). Sundays and Holy Days of Obligation (In the US: The Solemnity of Mary Mother of God, Ascension, Assumption, All Saints, Immaculate Conception, and Christmas) are always considered solemnities. Other examples of solemnities include the Solemnity of St. Joseph (March 19), and the Solemnity of the Sacred Heart of Jesus (Friday after the Feast of Corpus Christi).

Feasts are of secondary importance in our liturgical calendar and are celebrated on a particular day. These
feasts typically do not have a Vigil Mass on the prior evening. On these days, the Gloria is recited but not the Creed. An example of a feast is The Chair of Saint Peter the Apostle (February 22).

Next are memorials, which are either obligatory or optional. Memorials commemorate a saint or saints. Obligatory memorials must be observed whereas optional memorials do not have to be observed. For example, the memorial of St. John Bosco (January 31) is obligatory while the memorial of St. Blase February 3) is optional. Only the memorials of those saints who are of “universal significance” are observed by the whole Church and marked in the general liturgical calendar. The celebration of memorials is also governed by the liturgical season. For instance, obligatory memorials occurring during Lent are only celebrated as optional memorials.

(Source: Catholic Straight Answers)
Read more in the “Why Do We Do That?” series from Deacon Mike Fritz.