I found this excerpt helpful from a sermon by Charles Spurgeon on the above Beatitude:
“Other teachers had been content with outward moral reformation, but he(Jesus) sought the source of all the evil, that he might cleanse the spring from which all sinful thoughts, and words, and actions come. He insisted over and over again that, until the heart was pure, the life would never be clean. The memorable Sermon upon the mount, from which our text is taken, begins with the, benediction, “Blessed are the poor in spirit,” for Christ was dealing with men’s spirits, — with their inner and spiritual nature. He did this more or less in all the Beatitudes, and this one strikes the very centre of the target as he says, not ‘Blessed are the pure in language, or the pure in action,’ much less ‘Blessed are the pure in ceremonies, or in raiment, or in food;’ but ‘Blessed are the pure in heart.’ O beloved, whatever so-called “religion” may recognize as its adherent a man whose heart is impure, the, religion of Jesus Christ will not do so. His message to all men still is, “Ye must be born again;” that is to say, the inner nature must be divinely renewed, or else you cannot enter or even see that kingdom of God which Christ came to set up in this world. If your actions should appear to be pure, yet, if the motive at the back of those actions should be impure, that will nullify them all. If your language should be chaste, yet, if your heart is reveling in foul imaginations, you stand before God not according to your words, but according to your desires; according to the set of the current of your affections, your real inward likes and dislikes, you shall be judged by him. External purity is all that man asks at our hands, ‘for man looketh on the, outward appearance, but the Lord looketh on the heart;’ and the promises and blessings of the covenant of grace belong to those who are made pure in heart, and to none, besides.”