In the most basic sense, a
someone.
To get into some of the meat and potatoes of theology and traditional theological language on the subject:
There are two Greek words that are important here, and important to understand how they are used when talking about the Trinity. They are hypostasis (plural hypostases) and prosopon (plural prosopa). Both terms can be translated as "person" in English, though it requires some unpacking.
Hypostasis is translated into Latin as subsistentia, which becomes the English word subsistence. The word is formed from a combination of the prefix hypo, meaning "under" and the word stasis, meaning "to stand"; which is also basically what the Latin translation means as well. In the context of the Trinity it refers to the distinct and concrete reality of each of the Trinity. So the Father is the Father, the Son is the Son, the Holy Spirit is the Holy Spirit. Taking the Father as an example, the Father is real, rather than just a name or title, He is distinct, concrete reality in distinction to the Son and the Holy Spirit. That means the Father relates to and with the Son and the Spirit, the Father has begotten the Son, the Father spirates the Spirit. And so on and so forth. So the Three of the Trinity are real, the Three-ness of the Trinity is real. There really are Three, each distinct and real in Himself. The Father is Himself, the Father who has begotten the Son; the Son is Himself, the Son who is begotten of the Father; and the Holy Spirit is Himself, the Spirit of the Father and the Son who proceeds from the Father [and the Son*].
Prosopon is most clearly the word that corresponds with the English word "person", it is this word that is translated into Latin as persona (plural personae) which becomes the English word "person". This word, in antiquity, was tricky. In the ancient Greek world it referred to the "mask" or "role" an actor took on in a play. The ancient heretical position known as Sabellianism or Modalism (more properly, Modalistic Monarchianism) argued that God was a single Hypostasis with three prosopa; essentially they believed that God was one "person" who wore three different masks, or expressed Himself in three different roles in the way God related to the world. The Modalists believed that Jesus was God the Father in the flesh basically. This is heretical, it denies the relationality of the Three and makes a mess of Scripture so it was, quite rightly, condemned in antiquity. In modern times the Oneness Pentecostals (as opposed to the orthodox Trinitarian Pentecostals) hold views very similar. Because of this, the word prosopon to refer to the three Hypostases of the Trinity was a bit controversial, but accepted ultimately when defined properly in an orthodox way: That each prosopon of the Trinity is HImself a fully real person, a someone. Like Hypostasis, the Father is really Himself, the Son is really Himself, and the Holy Spirit is really Himself; each is distinctly and really HImself, so each is real and distinct. Not merely a "mask" or "face" or "role", but is truly and actually real in Himself.
So when we speak of Three Divine Persons of the Trinity we are saying there are three Someones. There is the Father, and He is real, He is Himself, He relates to and with the Son and the Holy Spirit; the same with the Son who is Himself and He relates with the Father and the Spirit, and likewise with the Spirit. There is a living, real, dynamic relationship within the undivided Divine Being and Essence. God is a Divine
Trinity of Persons. There is a Tri-Unity of God; there are Three, each is Himself, and each is truly and really God. The Father is God, the Son is God, and the Holy Spirit is God; not as three gods, but as one undivided God.
The Father is God, Maker of heaven and earth, of all things seen and unseen.
The Son is God, through whom all things were made, eternally begotten of the Father, of the Father's own Being, truly God of truly God, uncreated but begotten of the Father.
The Holy Spirit is God, eternally proceeding from the Father [and the Son*], who with Father and the Son is to be worshiped and glorified as true and very Lord and God.
Each is God, the one and only God.
Each is Lord, the one and only Lord.
Each is Almighty, the one and only Almighty.
Each is Eternal, the one and only Eternal.
Three Divine Persons, one God.
Three Divine Persons, equal in eternity, equal in glory and majesty, equal in Divinity.
*The expression "and the Son" is placed in brackets when speaking of the procession of the Holy Spirit due to the historic controversy over this term as it pertains to the ways the West and the East speak about the Trinity. The phrase was added to the Nicene Creed in the 11th century, and was a major contributing factor behind the Great Schisms of 1054 which led to the break in communion between the Western Church and the Eastern Church. This is known as the Filioque Controversy, with Filioque being the Latin word translated as "and the Son". The West maintains that the Holy Spirit proceeds from the Father and the Son; whereas the East maintains the Holy Spirit proceeds from the Father only. So as to try and maintain a semblance of neutrality, I'm following the common practice of including this expression in brackets.
-CryptoLutheran