These are some initial ideas about purity of heart taken from an excellent book on the spiritual life. Time permitting, I will add minimal commentary, perhaps by way of editing after the initial posting, but the main ideas are clear and simple enough.
Purity of Heart: Its nature and its properties
I. In what purity of heart consists.
Purity of heart consists in having nothing therein which is, in however small a degree, opposed to God and the operation of His grace.
All the creatures there are in the world, the whole order of nature as well as of grace, and all the leadings of Providence, have been so disposed as to remove from our souls whatever is contrary to God. For never shall we attain unto God until we have corrected, cut off, and destroyed, either in this life or in the next, everything that is contrary to God.
II. How necessary purity of heart is to us.
The first means towards the attainment of perfection is purity of heart; by it alone a St. Paul Hermit, a St. Mary of Egypt, and so many other holy solitaries attained thereto. Next after purity of heart come the precepts and spiritual doctrine to be found in books; then direction and faithful co-operation with graces bestowed. This is the high road of perfection.
We must devote our whole care to purifying our heart, because there lies the root of all our evils.
To be able to conceive how requisite purity of heart is to us, it would be necessary fully to comprehend the natural corruption of the human heart. There is in us a very depth of malice, which we do not perceive, because we never seriously examine our own interior. If we did, we should find therein a multitude of desires and irregular appetites for the honors, the pleasures, and the comforts of the world unceasingly fermenting in our heart.
We are so full of false ideas and erroneous judgments, of disorderly affections, passions, and malice, that we should stand confounded at ourselves could we see ourselves such as we are. Let us imagine ourselves a muddy well, from which water is continually being drawn; at first, what comes up is scarcely anything but mud; but by dint of drawing, the well is gradually cleansed, and the water becomes purer, until at last it is as clear as crystal. In like manner, by laboring incessantly to purge our soul, the ground of it becomes gradually cleared, and God manifests His presence by powerful and marvelous effects which He works in the soul, and through it, for the good of others.
When the heart is thoroughly cleansed, God fills the soul and all its powers, the memory, the understanding, and the will, with His holy presence and love. Thus purity of heart leads to union with God, and no one ordinarily attains thereto by other means.