St. Thomas Aquinas, in Summa Theologia II-II q. 83 a. 12 ("Whether prayer should be vocal?") c., writes:
Prayer is twofold, common and individual. Common prayer is that which is offered to God by the ministers of the Church representing the body of the faithful: wherefore such like prayer should come to the knowledge of the whole people for whom it is offered: and this would not be possible unless it were vocal prayer. Therefore it is reasonably ordained that the ministers of the Church should say these prayers even in a loud voice, so that they may come to the knowledge of all.
On the other hand individual prayer is that which is offered by any single person, whether he pray for himself or for others; and it is not essential to such a prayer as this that it be vocal. And yet the voice is employed in such like prayers for three reasons. First, in order to excite interior devotion, whereby the mind of the person praying is raised to God, because by means of external signs, whether of words or of deeds, the human mind is moved as regards apprehension, and consequently also as regards the affections. Hence Augustine says (ad Probam. Ep. cxxx, 9) that "by means of words and other signs we arouse ourselves more effectively to an increase of holy desires." Hence then alone should we use words and such like signs when they help to excite the mind internally. But if they distract or in any way impede the mind we should abstain from them; and this happens chiefly to those whose mind is sufficiently prepared for devotion without having recourse to those signs. Wherefore the Psalmist (Ps. 26:8) said: "My heart hath said to Thee: 'My face hath sought Thee,'" and we read of Anna (1 Kgs. 1:13) that "she spoke in her heart." Secondly, the voice is used in praying as though to pay a debt, so that man may serve God with all that he has from God, that is to say, not only with his mind, but also with his body: and this applies to prayer considered especially as satisfactory. Hence it is written (Osee 14:3): "Take away all iniquity, and receive the good: and we will render the calves of our lips." Thirdly, we have recourse to vocal prayer, through a certain overflow from the soul into the body, through excess of feeling, according to Ps. 15:9, "My heart hath been glad, and my tongue hath rejoiced."