The Red Heifer is the instrument through which a person is purified. The impurity of contact with death is the result of an encounter between a living person and death. A stone cannot cause ritual impurity, since it never had any life. Death is the opposite of life, and the shock of contact with it upsets life.
The severity of "tum'ah" – ritual impurity – is ranked according to the affinity between the individuals involved. A Jew who is dead causes impurity both by touch and by being in the same tent (or other structure). But a non-Jew can only pass on the impurity of death by direct contact.
Similarly, a woman who gives birth to a boy is impure for only seven days, because she carried within her a living body which left her. A woman who gives birth to a girl is impure for fourteen days, because in the future the female child will carry other life within her. Therefore the time of her impurity is twice the time for the birth of a boy.
Purification from the impurity of death takes place through the ritual of a Red Heifer, by a process of "resurrection."
"Let them take for you a completely red cow on which no yoke has been placed, and give it to Elazar the Priest, and let him slaughter it"[Bamidbar 19:2-3].
Let them take a cow for you: the word in Hebrew is "parah," from the root meaning fertility, but not a bull. When it is pregnant the cow gives more life than the bull. And it is a cow and not a sheep, in order that it will have extra vitality.
Red: This is the color of blood and of life.
Complete: This symbolizes complete and perfect life.
On which no yoke has been placed: In this way, it has never been diminished during its lifetime.
Let him slaughter it: Slaughtering is a cancellation of life.
"And let him burn it completely – its skin and its flesh, together with its blood and its dung." [19:5]. Everything is burned, even its waste.
Outside the camp: outside of the area of life. And it is transformed into ashes ("eifer"). As opposed to dust ("afar"), ashes cannot be used to grow anything and cannot be kneaded into a mixture. Ashes are something that remains separate from everything else.
Death also rules over the plant kingdom. The biggest of all trees is the cedar, and the smallest one is the hyssop. "And let the priest take some cedar wood and some hyssop, and a purple thread, and throw them into the fire of the cow." [19:8]. These two species are the opposite ends of the spectrum in the world of plants. "Tola'at," translated above as a thread, also means a worm. The cow and the worm are the opposite ends of the spectrum of animal life. And a worm is all that is left of a human being in the end.
Thus, the greatest examples of life have been transformed into symbols of death. They are all thrown into the fire of the cow.
A living person consists of a body and a soul. The body can be thought of as a sealed clay vessel. The soul is like an infinite flow of fresh water. Man can be thought of as a vessel which contains fresh water.
We take the ashes, the remainder of death, and we "resurrect" it using the fresh water of the soul, poured into a clay vessel, like the body. And that explains why this water is used to purify a person from the impurity of contact with death.
So, in the end, we have been able to explain the mystic inner meaning of the purification by the Red Heifer.
However, we might ask – If the matter is so simple, why did King Shlomo say, "I said I would be wise, but it is distant from me" [Kohellet 7:23]? (And we are taught that he was referring to the Red Heifer.)
The answer is that the secret remains hidden, in that it is not clear how life can rise up out of death. The secret of the transformation from death to life and from life to death is still beyond us. This is similar to the secret of how a living soul exists within the physical body, as the RAMA explained in commenting on the blessing recited after a person relieves himself: "And He acts in a wondrous way – He links a spiritual entity to a material object."