Our culture tries to see a separation between the physical and the spiritual that just isn't there. If you ever doubted that your physical being impacts your spiritual well-being, then this passage is for you. God ties the physical cleanliness to spiritual cleanliness and in so doing, he protected his people from disease, poor health, and environmentally based sicknesses of all kinds.
God charged the Levites with all of the major healthcare issues for the community as both the health department and doctor, in an era without any refrigeration. God had promised the people before they reached Sinai that if they would follow Him, he would not allow any of the diseases of the Egyptians to fall on them. This is how. Long before Louis Pasteur or Jonas Salk, God described how to deal with infectious illness. Before Dr. Oz, He was telling His people what was healthy to eat and what wasn't.
Eventually, the priesthood took things too far, but God's intention was that his people would be healthy, live long lives and have strong children. Since our bodies and minds are intimately related, His care for our bodies overflows into care for our minds and spirits. He leaves no details unaddressed. This is not surprising when you consider who He is. Since He made us, He should know best what it takes for us to live.
We are no longer bound by the law, but by Christ. However, understanding why these rules were put in place can go a long way toward maintaining a body, mind and spirit that can honor Him.