When Constantine the Great became Roman Emperor, he ended the persecution of Christians. As the first Christian Emperor, he favored Christians and assisted the Church in many ways. In AD 325, he convoked the first Council of the whole Church in the city of Nicea on the Aegean coast of what is today Turkey.
The main business of this Council was to attempt to resolve the controversy swirling around the teaching of Arius, a presbyter (elder, priest) of Alexandria. The nub of his teaching is that Christ was LIKE God (homoiousios), but not God in the SAME sense that God the Father was God (homoousios). His main opponent was the deacon Athanasius, who insisted that the incarnate Christ was fully God.
Athanasius's arguments carried the day, and the first version of the Creed was written to confute the errors of Arius; however, another generation of controversy followed. Eventually, the Council of Constantinople in 380 revised the Creed, strengthening its framework especially to emphasize the co-divinity of the Holy Spirit. This is the Creed we have today.
Much later, some Spanish Christians began adding "and the Son" (filioque) to the Creed, in order to emphasize the essential divinity of the Son. They did this without authorization of the whole Church, though the expression spread throughout the Western (Latin-speaking) Church, where it gained general acceptance over time. In the Eastern (Greek-speaking) Church, it never achieved acceptance, and this expression has been a source of division between Western and Eastern Christianity to this day.
THE NICENE CREED
We believe in one God,
the Father, the Almighty,
maker of heaven and earth,
of all that is, seen and unseen.
Note that the creative power of God is absolute. There are no unseen powers that are emanating from him to be demiurges, as in Neo-Platonist metaphysics, nor is he native to any unseen realm not of his making.
We believe in one Lord, Jesus Christ,
the only Son of God,
eternally begotten of the Father,
God from God, Light from Light,
true God from true God,
begotten, not made,
of one Being with the Father.
These expressions are piled onto each other in order to rule out any possible way of describing God the Son as being less God than God the Father. The expression "light from light" carries the double meaning that God is Light -- and so therefore is the Son of God -- but also that the mode of his begetting is like that of light from a candle. The ray of light is produced by the flame, but one does not exist before the other: so the Father begets the Son, but the Father is not prior to the Son.
Through him all things were made.
The Son is the agent of creation. See also Gospel of John, Chapter 1: "and without him was not anything made that was made."
For us and for our salvation
he came down from heaven:
by the power of the Holy Spirit
he became incarnate from the Virgin Mary,
and was made man.
For our sake he was crucified under Pontius Pilate;
he suffered death and was buried.
On the third day he rose again
in accordance with the Scriptures;
he ascended into heaven
and is seated at the right hand of the Father.
He will come again in glory to judge the living and the dead,
and his kingdom will have no end.
This section covers the work of the incarnate Jesus, the Christ.
We believe in the Holy Spirit, the Lord, the giver of life,
who proceeds from the Father and the Son.
With the Father and the Son he is worshiped and glorified.
He has spoken through the Prophets.
The Holy Spirit is as much God as the Father and the Son, hence the divine titles. The procession of the Holy Spirit from the Son (as well as the Father) is the point at issue, above, between Eastern and Western Christians.
N.B. I have used the Western version of the Creed since I am a son of the Western Church; a fair-minded Eastern Christian would note the addition and controversy surrounding it, but probably put it in a footnote rather than the body of the Creed, where he does not think it belongs.
We believe in one holy catholic and apostolic Church.
We acknowledge one baptism for the forgiveness of sins.
We look for the resurrection of the dead,
and the life of the world to come. Amen.
The Creed asserts the unique character and necessity of the Church and her rites, and looks forward to the Day when God will restore all things.
Note that the Apostles' Creed begins, "I believe," while the Nicene Creed begins "We believe." After the Council of Nicea, most local churches used the simpler Creed (or a similar one) in their baptismal rites; indeed, only in the new diocese of Constantinople was the Nicene Creed used as a baptismal creed. The reason for this is that the Nicene Creed is not a baptismal creed, but a teaching creed, meant to provide a standard for the teachers of the faith. If you can't make heads or tails of its technicalities, that doesn't mean there's something wrong with you. But if you were to apply to be a minister or priest, most Churches have historically demanded that their clergy understand and affirm the orthodoxy expressed in the Nicene Creed.
There is, of course, much more to Nicene orthodoxy than I have set forth here. But for those new to Christianity (or new to theology), this brief explanation may be of assistance.