The Apostle's Creed is the ancient creed of Baptism. Since Advent is the beginning of the Church year, it is appropriate to begin by reminding ourselves of our Baptism into the Church. The Apostle's Creed is the answer to a series of questions asked of candidates for Baptism.
The Nicene Creed is a fuller statement of faith, which addresses several heresies, especially Arianism. Almost all Christian denominations recite the latter on Sundays, because it is the universal creed of what all Christians are supposed to believe--that Christ was the only begotten Son of God; that He is not created; of the same substance of the as the Father, and truly God and truly man.
Eastern Orthodoxy differs from Catholic doctrine on the nature of the Holy Spirit. In the Eastern Church, the Holy Spirit proceeds from the Father, only. In the Western church, He proceeds from the Father and from the Son.
In the Nicene Creed we bow, or genuflect at the Incarnatus, or the statement that Christ was born of the Blessed Virgin and became man. This is the great miracle for which we should have great reverence and gratitude, because it is the ultimate expression of God's love for humanity.
Advent is the season of preparation for Christmas. Note that the liturgical colors used are purple (or in some cases blue). It is not Christmas. It is a penitential season. Christmas is a celebratory season, and consists of 12 days, beginning with the Feast of the Nativity, as described in other posts in this thread. (If you were paying attention, you might have noticed that the lectionary readings for the last two weeks of Ordinary time are Advent-like. This is because, long ago, Advent was six-weeks long, not four, as is now the case.)
This is all off the top of my balding head. You can find fuller explanations elsewhere on this site.