I do believe in the unity of the Holy Trinity, however, I just do not seem to get it. Could you please explain it?
The "Trinity" is God the Father, and His Son, and His Holy Spirit. The "Trinity" is one in essence and is undivided. God revealed the mystery of the Holy Trinity at the Lord Jesus Christ's Baptism. Please read the Holy Gospel of St. Matthew 3:13-17. The Father speaks; the Holy Spirit descends; the incarnate Son is baptized and anointed.
Of course it is very hard to try to understand and comprehend the Unlimited God with our limited minds. But to simplify it we can say, "we believe in one God, existing by Himself (the Father), and speaking through His Word (the Son or the Logos) and living by His Spirit (the Holy Spirit).
In the Old Testament we are given references to the Holy Trinity. The Triple Holy Hymn sung by the angels in Isaiah's vision (Isaiah 6:1-4) suggests one God in three persons.
Also please read the Holy Gospel of St. Matthew 28:19 in which the disciples were to be baptized in the name of the Father, the Son, and the Holy Spirit.
Further, God the Father is one of the three persons of the Holy Trinity. God the Son is eternally begotten of God the Father. God the Holy Spirit eternally proceeds from God the Father.
Suggested reading for this subject includes a book written by His Holiness Pope Shenouda, "The Divinity of Christ".