The chief concern was that of the Arian Heresy. Arius, a bishop of the Church, had been spreading his doctrine that Jesus Christ was not actually God. This was indeed problematic, for if Jesus is not God, he cannot save us and his sacrifice becomes meaningless. Clearly this was against the understanding of the rest of the early Church. However, the Church had never explicitly needed to define its views on the matter, since they were simply accepted.
The division in the Church caused by Arius was very damaging, with rival factions claiming to be the "true" Christians - even the bishops were divided. After much discussion and theological debate, the Council declared that Jesus was indeed God (the term used was homoousia, which means 'of the same substance'). Thus, the doctrine of a Trinitarian God was defined. This does not mean that God was not a Trinity of Three Divine Persons before the Council said so, it means that the Council needed to explain God as such to quell a controversy. The word 'trinity' of course, is nowhere in the Bible, but neither are 'incarnation', 'transubstantiation' or 'sacrament.' Words help us grasp the nature and action of God in a concrete way.
Long story short, the most memorable thing that came out of the Council of Nicaea was the Nicene Creed, a summary statement of Christian belief. As I reflect on it more and more, its theological richness becomes increasingly apparent. Each time we recite this, our core beliefs and dogmas, at Sunday mass, I am reminded that the Faith is timeless. People have recited this Creed and believed these things in times and places far removed from 21st Century America. That just helps me remember the universality (the meaning of the word 'catholic') of the Church and her message.
For your perusal, the Nicene Creed in both Latin and English:
Credo in unum Deum, Patrem omnipotentem, factorem caeli et terrae, visibilium omnium et invisibilium.
Et in unum Dominum Iesum Christum, Filium Dei unigenitum, et ex Patre natum ante omnia saecula. Deum de Deo, Lumen de Lumine, Deum verum de Deo vero, genitum non factum, consubstantialem Patri; per quem omnia facta sunt. Qui propter nos homines et propter nostram salutem descendit de caelis. ET INCARNATUS EST DE SPIRITO SANCTO EX MARIA VIRGINE, ET HOMO FACTUS EST. Crucifixus etiam pro nobis sub Pontio Pilato, passus et sepultus est, et resurrexit tertia die, secundum Scripturas, et ascendit in caelum, sedet ad dexteram Patris. Et iterum venturus est cum gloria, iudicare vivos et mortuos, cuius regni non erit finis.
Et in Spiritum Sanctum, Dominum et vivificantem, qui ex Patre Filioque procedit. Qui cum Patre et Filio simul adoratur et conglorificatur: qui locutus est per prophetas. Et unam, sanctam, catholicam et apostolicam Ecclesiam. Confiteor unum baptisma in remissionem peccatorum. Et expecto resurrectionem mortuorum, et vitam venturi saeculi. Amen.
Now, enjoy Mozart's rendition of the Creed from his Coronation Mass in C-Major. The video is from a mass inside St. Peter's, Rome.