3 Now I remember that I promised to consider in this Psalm with what suitableness the moon signifies the Church. There are two probable opinions concerning the moon: but of these which is the true, I suppose it either impossible or very difficult for a man to decide. For when we ask whence the moon has her light, some say that it is her own, but that of her globe half is bright, and half dark: and when she revolves in her own orbit, that part wherein she is bright gradually turns towards the earth, so as that it may be seen by us; and that therefore at first her appearance is as if she were horned....According to this opinion the moon in allegory signifies the Church, because in its spiritual part the Church is bright, but in its carnal part is dark: and sometimes the spiritual part is seen by good works, but sometimes it lies hid in the conscience, and is known to God alone, since in the body alone is it seen by men....But according to the other opinion also the moon is understood to be the Church, because she has no light of her own, but is lighted by the only-begotten Son of God, who in many places of holy Scripture is allegorically called the Sun. Whom certain heretics being ignorant of, and not able to discern Him, endeavour to turn away the minds of the simple to this corporeal and visible sun, which is the common light of the flesh of men and flies, and some they do pervert, who as long as they cannot behold with the mind the inner light of truth, will not be content with the simple Catholic faith; which is the only safety to babes, and by which milk alone they can arrive in assured strength at the firm support of more solid food. Whichever then of these two opinions be the true, the moon in allegory is fitly understood as the Church. Or if in such difficulties as these, troublesome rather than edifying, there be either no satisfaction or no leisure to exercise the mind, or if the mind itself be not capable of it, it is sufficient to regard the moon with ordinary eyes, and not to seek out obscure causes, but with all men to perceive her increasings and fulnesses and wanings; and if she wanes to the end that she may be renewed, even to this rude multitude she sets forth the image of the Church, in which the resurrection of the dead is believed.
Source: The Enarrations, or Expositions, on the Psalms (New Advent)