Rather than "define Trinity" we can go directly to Scripture and confirm that:
THE FATHER IS GOD
THE SON IS GOD
THE HOLY SPIRIT (HOLY GHOST) IS GOD
THE FATHER IS GOD
Grace be unto you, and peace, from God our Father, and from the Lord Jesus Christ. (1 Cor 1:3).
THE SON IS GOD
But unto the Son he saith, Thy throne, O God, is for ever and ever: a sceptre of righteousness is the sceptre of thy kingdom. Thou hast loved righteousness, and hated iniquity; therefore God, even thy God, hath anointed thee with the oil of gladness above thy fellows. And, Thou, Lord, in the beginning hast laid the foundation of the earth; and the heavens are the works of thine hands: (Heb 1:8-10).
THE HOLY SPIRIT IS GOD
But Peter said, Ananias, why hath Satan filled thine heart to lie to the Holy Ghost, and to keep back part of the price of the land? Whiles it remained, was it not thine own? and after it was sold, was it not in thine own power? why hast thou conceived this thing in thine heart? thou hast not lied unto men, but unto God. (Acts 5:3-4).
So, because all three Divine Persons are God, we have the triune Godhead (or Trinity). WE could list numerous other passages to establish this doctrine.