The mystery of the Trinity may be compared to the sun -- when I stare into the sun, I am blinded; but by that same overwhelming light, all reality is illumined and made intelligible to me. So also, when I see to understand the Trinity, my mind is dazed and I am overwhelmed; but it is the love of the Trinity which has revealed to me all the other mysteries of our Faith.
The Trinity is one God in three Persons, three Persons in one Nature. But what do we mean by "Person" and "nature"? Person answers the question of "who?", while nature answers the question of "what?" -- in the Trinity there are three "Whos" (the Father and the Son and the Holy Spirit) and one "What" (one God).
Reflecting further, we see that, because there is only one God and one divine Nature, the three Persons have only one Divine Intellect (one Divine Knowledge) and one Divine Will (one Divine Love). This means that there is no subordination in the Trinity, the Father is not greater than the Son nor is the Son less than the Father. Neither is there any obedience within the Trinity, the Son does not obey the Father because the Son has no personal will/desire he could subject to the personal will/desire of the Father - the Divine Will of the Son is the Divine Will of the Father.
However, we compare this to the mystery of the Incarnation: In the Trinity, we have three Persons in one Nature; but, in the Incarnation, we have one Person in two Natures. Thus, in Christ, we have a Divine Nature and an human nature, but only one Divine Person. Hence, Jesus has a Divine Intellect (Divine Knowledge, which is one with the Father and the Holy Spirit) and an Human Intellect (human knowledge, which is proper to Jesus in his humanity). Likewise, the Lord has a Divine Will (one with the Father and the Holy Spirit), and an human will (in his humanity).
In this way, Jesus is obedient to the Father in his human nature -- the Lord submits his human will to the Divine Will; which means he is obedient as man also to himself as God, and to the Holy Spirit.
In his Love for us, God the Father sends his Son and the Holy Spirit invisibly into our hearts by grace. And this is sanctifying grace, the created participation in the Life of the Trinity within us.
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