Whenever we pray, it can seem that it is only our brain that prays, as the mind instructs our lips in the words to say.
However, Christian tradition goes beyond the scientific view of the human person and states that prayer comes from the heart.
The Catechism of the Catholic Church begins its section on prayer with a quote from St. Thérèse of Lisieux that summarizes this idea:
For me, prayer is a surge of the heart; it is a simple look turned toward heaven, it is a cry of recognition and of love, embracing both trial and joy.
The heart
The idea of prayer coming from the heart is expanded on in the following paragraph in the Catechism:
Where does prayer come from? Whether prayer is expressed in words or gestures, it is the whole man who prays. But in naming the source of prayer, Scripture speaks sometimes of the soul or the spirit, but most often of the heart (more than a thousand times). According to Scripture, it is the heart that prays. If our heart is far from God, the words of prayer are in vain.
The Church does not refer to an organ in our body, but to our "spiritual" heart:
The heart is the dwelling-place where I am, where I live; according to the Semitic or Biblical expression, the heart is the place "to which I withdraw." The heart is our hidden center, beyond the grasp of our reason and of others; only the Spirit of God can fathom the human heart and know it fully. The heart is the place of decision, deeper than our psychic drives. It is the place of truth, where we choose life or death. It is the place of encounter, because as image of God we live in relation: it is the place of covenant.
Whenever we pray, we should dwell on this reality and reflect on where our heart truly is and if it is in union with God.