All Apostolic Churches, like Anglicans, Old Catholics, and the Vatican Catholics, all have liturgical seasons. Most Mainline Protestants as well, such as Presbyterians, Methodists, and the Disciples of Christ (Christian Church). Many Evangelical Protestants don't and I've never heard of a Fundamentalist Protestant group that does.
Liturgical seasons were based on how Holy Scripture was read in the churches. The first real recognized season is the one we just started, Lent, which was a 40 day journey with Christ in the desert. It was time of fasting, penitence, and abstinance as well as increased devotion and prayer. A mini season of Holy Week celebrated the last week of Jesus' life, which includes the Holy Triduum, or Holy Tree Days, specifically recounting the events of the Last Supper to His time in hades/sheol. Lent ends on Holy Saturday around 6:00pm with the Great Paschal Vigil, beginning the Easter season.
Other seasons later developed, like Advent, Christmas, and Pentecost Week.
Advent -> Christmas -> Epiphany -> Lent (Holy Week is the last week; Holy Triduum is the last three days) -> Easter (first week is Bright Week) -> Pentecost Week -> Kingdom Tide (or Ordinary Time or Season After Pentecost or Trinity Tide...includes All Hallow's Tide, which is Oct. 31 - Nov. 2) -> Advent, etc.