Objection 1. It would seem that a vow is not solemnized by the reception of holy orders and by the profession of a certain rule. As stated above (Article 1), a vow is a promise made to God. Now external actions pertaining to solemnity seem to be directed, not to God, but to men. Therefore they are related to vows accidentally: and consequently a solemnization of this kind is not a proper circumstance of a vow.
Objection 2. Further, whatever belongs to the condition of a thing, would seem to be applicable to all in which that thing is found. Now many things may be the subject of a vow, which have no connection either with holy orders, or to any particular rule: as when a man vows a pilgrimage, or something of the kind. Therefore the solemnization that takes place in the reception of holy orders or in the profession of a certain rule does not belong to the condition of a vow.
Objection 3. Further, a solemn vow seems to be the same as a public vow. Now many other vows may be made in public besides that which is pronounced in receiving holy orders or in professing a certain rule; which latter, moreover, may be made in private. Therefore not only these vows are solemn.
On the contrary, These vows alone are an impediment to the contract of marriage, and annul marriage if it be contracted, which is the effect of a solemn vow, as we shall state further on in the Third Part of this work [Supplement, 53, 2].
I answer that, The manner in which a thing is solemnized depends on its nature [conditio]: thus when a man takes up arms he solemnizes the fact in one way, namely, with a certain display of horses and arms and a concourse of soldiers, while a marriage is solemnized in another way, namely, the array of the bridegroom and bride and the gathering of their kindred. Now a vow is a promise made to God: wherefore, the solemnization of a vow consists in something spiritual pertaining to God; i.e. in some spiritual blessing or consecration which, in accordance with the institution of the apostles, is given when a man makes profession of observing a certain rule, in the second degree after the reception of holy orders, as Dionysius states (Eccl. Hier. vi). The reason of this is that solemnization is not wont to be employed, save when a man gives himself up entirely to some particular thing. For the nuptial solemnization takes place only when the marriage is celebrated, and when the bride and bridegroom mutually deliver the power over their bodies to one another. On like manner a vow is solemnized when a man devotes himself to the divine ministry by receiving holy orders, or embraces the state of perfection by renouncing the world and his own will by the profession of a certain rule.
Reply to Objection 1. This kind of solemnization regards not only men but also God in so far as it is accompanied by a spiritual consecration or blessing, of which God is the author, though man is the minister, according to Numbers 6:27, "They shall invoke My name upon the children of Israel, and I will bless them." Hence a solemn vow is more binding with God than a simple vow, and he who breaks a solemn vow sins more grievously. When it is said that a simple vow is no less binding than a solemn vow, this refers to the fact that the transgressor of either commits a mortal sin.
Reply to Objection 2. It is not customary to solemnize particular acts, but the embracing of a new state, as we have said above. Hence when a man vows particular deeds, such as a pilgrimage, or some special fast, such a vow is not competent to be solemnized, but only such as the vow whereby a man entirely devotes himself to the divine ministry or service: and yet many particular works are included under this vow as under a universal.
Reply to Objection 3. Through being pronounced in public vows may have a certain human solemnity, but not a spiritual and divine solemnity, as the aforesaid vows have, even when they are pronounced before a few persons. Hence the publicity of a vow differs from its solemnization.
Source: Summa Theologica (New Advent)