After the perfection of charity has been set forth, the Lord now teaches how righteousness is to be practiced without corruption. For even good works may be spoiled if they are done for the sake of human praise. Therefore He begins by warning that righteousness itself must be guarded, lest it be emptied of its reward by the desire of being seen.

The alms of the hypocrite are not condemned because they are given, but because they are given to be observed. For when the eye of the heart is turned toward human approval, the work that appears good outwardly is inwardly corrupted. Such men have already received what they sought, since they desired the praise of men and obtained it; but they do not seek, and therefore do not receive, the reward of the Father.

The image of the trumpet signifies ostentation rather than sound, for they make a display of mercy as though it were something extraordinary, desiring to be admired rather than to relieve the needy. The Lord does not forbid almsgiving in public places, but He forbids the intention of seeking glory from it.

When He says that the left hand should not know what the right hand does, He teaches that even inward self-congratulation is to be avoided. For the right hand signifies the intention of doing good, while the left hand signifies the delight taken in one’s own action. Thus alms are done in secret when the heart does not turn back upon itself to take pleasure in what it has done.

The Father who sees in secret rewards openly, not because He was ignorant before, but because what was hidden from men is then made manifest by divine recompense. In this way the Lord orders the soul to act rightly for God alone, teaching that true righteousness seeks no witness except Him who sees all things and whose reward alone endures.

Source: St. Augustine, On the Lord’s Sermon on the Mount,  Book II, Chapters 1-2