Who proceedeth from the Father
The line of the Nicene creed comes straight from John 15:26, “But when the Helper comes, whom I will send to you from the Father, the Spirit of truth, who proceeds from the Father, he will bear witness about me.” Just as we discussed regarding the Son, the second person of the Trinity is eternally begotten (not made) Son of God. The Holy Spirit, the third person of the Trinity eternally proceeds from the Father and the Son (more on the ‘Filioque’ Clause next week). The Holy Spirit is not the begotten Son of God but proceeds from the Father and the Son. The addition to the Nicene-Constantinople Creed was to clarify the deity of the Holy Spirit. The Holy Spirit is the same essence as the Father and the Son. The difference of generation and procession can be confusing to some, even great scholars (Eg John of Damascus, Augustine to name two). Francis Turretin gives three main differences  (which I will not go into here). The Westminster Confession puts it this way, “the Father is of none, neither begotten, not proceeding; the Son is eternally begotten of the Father; the Holy Ghost eternally proceeding from the Father and the Son” (WCF 2.3).
Quite simply the eternal procession of the Spirit teaches two important theological points the first is the Holy Spirit is God. He has the same essence as the other two persons of the godhead. He is a Spirit, infinite, eternal, and unchangeable, in his being, wisdom, power, holiness, justice, goodness, and truth (WSC 4). The second aspect is that The Holy Spirit is not the Father nor the Son. No person of the Trinity is made or created (hence eternal), the Father is of none, the Son is begotten of the Father and the Holy Spirit proceeds from the Father and the Son. All three persons of the triune God all have the same essence, and they are God.
This is where we get the language of first, second and third when referring to the persons of the Trinity. It is not in order of authority, power, or submission, nor is it in created order (because all three persons are eternal). The three persons in the Godhead; the Father, the Son, and the Holy Spirit are one God, the same in substance, equal in power and glory (WSC 6). The Father is of none (First), the Son begotten from the Father (Second), and the Holy Spirit proceeds from the Father and the Son (Third).