The sixth Beatitude is often translated using "pure" instead of "clean", regardless, the intention is still the same. Jesus isn't concerned about out physical organ, but the place from which we make decisions and see the world. It would make more sense to replace the word "heart" with "soul", because we are being encouraged to strive for a soul that is clean or pure; free from sin.
Wow. That's a tall order, a life free from sin. But Jesus understands the difficulty of our human experience, and rather than asking us to live sin-free, He asks to have a clean heart. A heart with good intentions. This Beatitude, buried in the middle of the rest, is actually the guiding force of all the others! A clean heart enables us to live for God! It empowers us to see beyond our earthly needs and answer God's call each day. A clean heart goes beyond the Jewish tradition of clean and unclear (lepers, certain foods and actions) but deep into the root of the human being.
And that right there is what Jesus's big message really was. It was an invitation for the Jewish people to live their faith beyond the rules they had constructed for themselves and live intentionally. Similarly, Catholics frequently stumble on our own rules too. We have to attend Mass on Sundays and Holy Days, we must go to confession once a year, we are required to abstain from meat on Fridays during Lent, all the while forgetting the intention behind those actions. Instead of checking religious off of a list, we should focus on our own hearts and simply come to Him, and in doing so, see God.
In Matthew 19: 13-15, we are given a beautiful example of clean hearts, who come to Christ eagerly, not because they have to but because they want to. Read over that short passage today and ask yourself, do you come to Jesus with an open heart and good intention. Or is your faith life a life of checking off boxes and going through the motions, because it is what we "supposed to do"?