It means that God is a Father, Son, and Holy Spirit, just like a man can be a father, son, husband, lawyer, and other things, all at once. The Father is the Creator. The Son is Jesus Christ. The Holy Spirit is God when he speaks to us.
I would word it:
The Father is a distinct personage, with distinct functions within the Triune, co-equal Singular Deity known as GOD;
The Son is a distinct personage, with distinct functions within the Triune, co-equal Singular Deity known as GOD;
The Holy Spirit is a distinct personage, with distinct functions within the Triune, co-equal Singular Deity known as GOD.
The analogy that I like to use when people seem to not understand how the Three can be ONE GOD is:
We are created in the image of GOD. Yet there is only ONE WAY that we are anything like GOD in how we were formed in our mothers womb. We have three distinct parts that make up ONE human Being, just like God has three Distinct Personages that make up One Divine Being. We have a Body, a Soul, and a Human Spirit that make up ONE HUMAN BEING. Notice two of the Parts are invisible and only one is Visible just like GOD.
1 Thessalonians 5:23 (NRSV)
[SUP]
23 [/SUP] May the God of peace himself sanctify you entirely; and
may your spirit and soul and body be kept sound and blameless at the coming of our Lord Jesus Christ.