We are made in the image of the Trinity as St. Augustine says as well. One analogy (and no analogy is perfect especially when coming to the Trinity since full understanding of the Trinity is beyond human understanding) is that the Father is like your memory, the Son is your word and the Holy Spirit is your will.
Right now you are just interacting with my words, as I am with you, but I wouldn't say that I'm not interacting with you. The word of God is fully God, and my words (ideally) fully represent me.
Similarly if a person loses their memories, they lose what it is to be them, even though they might still have words. An example of course is dementia.
This also carries on when you interact with an action of someone. A person who cannot act is not themselves either anymore, but interacting with their actions is interacting with them.
A slightly different organization or mapping of this would be the Father as being your subconscious mind and the Son as your conscious mind. The Logos or the Son is often called as the Mind of God, but it seems to be the rational conscious mind of God. The invisible unknowable God without the Word is like our subconscious. We ourselves can only know our mind through thinking words, through literal words in our mind but also our conscious mind.
Anyways it has been understood by many Saints going back to St. Augustine, that man was created in the image of the Trinity, and this is an example of how it can be so.