The Red Heifer is actually a rather simple ritual. Death, the result of man’s original sin in Eden and the ultimate insult to our spiritual immortality; makes us ritually impure and is in need of an antidote. The Red Heifer is that antidote.
The sacrificial cult and culture contained in the Hebrew Bible provides the mother of all sacrifices, an unblemished red cow, which is to be sacrificed, and whose ashes are to be mixed with water and sprinkled by a priest onto those defiled by contact with the dead. End of story.
But for reasons to be explored below, the Red Heifer represents THE puzzling paradox of the Jewish Religion. (Numbers 19: 2-10)
This is the statute of the law which the LORD hath commanded, saying: Speak unto the children of Israel, that they bring thee a red heifer, faultless, wherein is no blemish, and upon which never came yoke.  And a man that is clean shall gather up the ashes of the heifer, and lay them up without the camp in a clean place, and it shall be kept for the congregation of the children of Israel for a water of sprinkling; it is a purification from sin. And he that gathereth the ashes of the heifer shall wash his clothes, and be unclean until the even; and it shall be unto the children of Israel, and unto the stranger that sojourneth among them, for a statute for ever.
זֹאת חֻקַּת הַתּוֹרָה, אֲשֶׁר-צִוָּה יְהוָה לֵאמֹר: דַּבֵּר אֶל-בְּנֵי יִשְׂרָאֵל, וְיִקְחוּ אֵלֶיךָ פָרָה אֲדֻמָּה תְּמִימָה אֲשֶׁר אֵין-בָּהּ מוּם, אֲשֶׁר לֹא-עָלָה עָלֶיהָ, עֹל.
וְכִבֶּס בְּגָדָיו הַכֹּהֵן, וְרָחַץ בְּשָׂרוֹ בַּמַּיִם, וְאַחַר, יָבֹא אֶל-הַמַּחֲנֶה; וְטָמֵא הַכֹּהֵן, עַד-הָעָרֶב.
וְהַשֹּׂרֵף אֹתָהּ–יְכַבֵּס בְּגָדָיו בַּמַּיִם, וְרָחַץ בְּשָׂרוֹ בַּמָּיִם; וְטָמֵא, עַד-הָעָרֶב.
וְאָסַף אִישׁ טָהוֹר, אֵת אֵפֶר הַפָּרָה, וְהִנִּיחַ מִחוּץ לַמַּחֲנֶה, בְּמָקוֹם טָהוֹר; וְהָיְתָה לַעֲדַת בְּנֵי-יִשְׂרָאֵל לְמִשְׁמֶרֶת, לְמֵי נִדָּה–חַטָּאת הִוא.
וְכִבֶּס הָאֹסֵף אֶת-אֵפֶר הַפָּרָה, אֶת-בְּגָדָיו, וְטָמֵא, עַד-הָעָרֶב; וְהָיְתָה לִבְנֵי יִשְׂרָאֵל, וְלַגֵּר הַגָּר בְּתוֹכָם–לְחֻקַּת עוֹלָם.
Rashi immediately goes on the defensive:
This is the statute of the Torah: Because Satan and the nations of the world taunt Israel, saying, “ What is this commandment, and what purpose does it have?” Therefore, the Torah uses the term “statute.” I have decreed it; You have no right to challenge it. — [Yoma 67b]
זאת חקת התורה; לפי שהשטן ואומות העולם מונין את ישראל לומר מה המצוה הזאת ומה טעם יש בה, לפיכך כתב בה חקה, גזירה היא מלפני ואין לך רשות להרהר אחריה
Sprinkling some water and “poof” your sins are washed away give us moderns the Heebie jeebies, but also seemed to trouble non-Jews of the 1st Century. (Pĕsikta Dĕ-Rab Kahăna, Chapter 4 Parah Aduma)
But what really made the Red heifer into a theological flash point was the fact that while it purified the impure, the priests involved with it’s preparation and with the sprinkling, were made impure.
מטהרת את הטמאים ומטמאה את הטהורים
[as formulated by Saadia Gaon, The Book of Beliefs and Opinions 3:10] 
It is hard to understand what made this paradox so perplexing. After all, if you take a glowing piece of molten metal and put it into a cold pot of water…. The water gets hot and the metal gets cool. In physics, we call this the law of conservation of energy which states that the total energy of an isolated system cannot change.
Which brings us to God and religion…
The Pĕsikta Dĕ-Rab Kahăna devotes a whole chapter to the Red Heifer and starts as follows:
What makes the Red Heifer so audacious is that ultimately it is God who purifies the world and according to the law of the Red Heifer (and the law of the conservation of energy) … God must become impure in the process.
This heresy lies behind the Lurianic Kabbalistic concept of Tzimtzum (צמצום contraction/constriction/condensation/withdrawal”) that God began the process of creation by “contracting” his infinite light in order to allow for a “conceptual space” in which finite and seemingly independent realms could exist. If God’s purity is in His infinite nature, then to allow a finite world to exist, He had to contract, or compromise His purity.
This heresy lies behind a lesser known concept sported by Maimonides known as the “gracious ruse” a concept perhaps borrowed from the second-century-C.E. philosopher Alexander of Aphrodisias who developed the theory of divine condescendence (Greek synkatabasis; cf. Arabic talattuf Hebrew: הערמה האלהית ibn tibbon ). Maimonides uses this concept of the Divine trick to explain why God permitted Judaism to be compromised with so many artifacts of paganism: “It was in accordance with the wisdom and plan of God (literally “gracious ruse”), as displayed in the whole Creation, that He did not command us to give up and to discontinue all these manners of service; for to obey such a commandment it would have been contrary to the nature of man. Part III, chapter 32
Ultimately, this is the heresy that gave birth to the concept that the suffering, even death of a holy person can purify and redeem the Chosen People. (read Isaiah 53 excerpted below )
He was despised, and forsaken of men, a man of pains, and acquainted with disease, and as one from whom men hide their face: he was despised, and we esteemed him not. Surely our diseases he did bear, and our pains he carried; whereas we did esteem him stricken, smitten of God, and afflicted. But he was wounded because of our transgressions; he was crushed because of our iniquities: the chastisement of our welfare was upon him, and with his stripes we were healed. All we like sheep did go astray, we turned everyone to his own way; and the LORD hath made to light on him the iniquity of us all. … Yet it pleased the LORD to crush him by disease; to see if his soul would offer itself in restitution אָשָׁם נַפְשׁוֹ, that he might see his seed, prolong his days, and that the purpose of the LORD might prosper by his hand: Of the travail of his soul he shall see to the full, even My servant, who by his knowledge did justify the Righteous One to the many, and their iniquities he did bear. Therefore will I divide him a portion among the great, and he shall divide the spoil with the mighty; because he bared his soul unto death, and was numbered with the transgressors; yet he bore the sin of many וְהוּא חֵטְא-רַבִּים נָשָׂא, and made intercession for the transgressors.
Of no surprise, scholars, even Jewish scholars, have seen this Suffering Servant as a precursor of the, initially Jewish expectation that a messiah will come who will die for our sins (see The Jewish Gospels: The Story of the Jewish Christ by Daniel Boyarin pp150-)
See also “Said R. Ammi, Wherefore is the account of Miriam’s death4 placed next to the [laws of the] red heifer?5 To inform you that even as the red heifer afforded atonement [by the ritual use of its ashes], so does the death of tie righteous afford atonement [for the living they have left behind]. (Moed Katan 28a)
It’s a slippery slope and a short walk to go one step further and require that not the messiah, but God Himself must commit the ultimate compromise and …. Die, so that we can live.
It’s no wonder that when Moses goes up to heaven to visit God he finds God studying the Torah portion of the Red Heifer!
When Moshe went up to the heights of heaven, he heard the voice of the Holy One, blessed be He, as He sat engaged in the study of the passage on the Red Heifer, citing a law in the name of the sage who stated it: “Rabbi Eliezer said: The heifer whose neck is to be broken must be [not more than] one year old; and the red heifer [not more than] two years old.”
Moshe said before the Holy One, blessed be He: “Master of the Universe, worlds above and worlds below are in Your domain, yet You sit and cite a law ascribed to flesh and blood!”
The Holy One, blessed be He, replied: “Moshe, there will arise in My world a righteous man who, [in his concern for the purification of Israel], will begin his instruction of the Oral Law with the passage on the red heifer, and so I, [also concerned for the purification of Israel], say: ‘Rabbi Eliezer said: The heifer whose neck is to be broken must be [not more than] one year old; and the red heifer [not more than] two years old.'” [Pĕsikta Dĕ-Rab Kahăna, Chapter 4] 
Fortunately for us Jews, Christianity took this heresy and ran with it. We Jews replaced the laws of the Red Heifer and the sacrificial cult with prayer and water works… washing our hands and dunking in the mikva (ritual bath). Mishna Yoma 8:10
Rabbi Akiva says: Fortunate are you O Israel! Before whom do you purify yourselves? [And] who purifies you? Your Father in Heaven! As it is said: “I will sprinkle upon you pure water and you shall become purified” (Ezekiel 36:25), and it is further said: “The hope [dewn] of Israel is the Lord” (Jeremiah 17:13), just as a mikvah purifies the defiled so too, does the Holy one Blessed is He, purify Israel
אָמַר רַבִּי עֲקִיבָא
לִפְנֵי מִי אַתֶּם מִטַּהֲרִין
וּמִי מְטַהֵר אֶתְכֶם
וְאוֹמֵר, (ירמיה יז) “מִקְוֵה יִשְׂרָאֵל יְיָ” –
מַה מִּקְוֶה מְטַהֵר אֶת הַטְּמֵאִים
אַף הַקָּדוֹשׁ בָּרוּךְ הוּא מְטַהֵר אֶת יִשְׂרָאֵל
Akiva changed the model. Unlike the water of the Red Heifer, the water of the ritual bath (mikveh) is not a zero sum game. The impurity removed from the impure in the mikveh is not transferred to the living water (בְּמַיִם חַיִּים) of the mikva (Leviticus 15:13), and so presumably God need not be compromised and made impure when He purifies His people.
Judaism may be a dirty business, but fortunately we have Akiba and God Himself reviewing the texts and massaging the data. As for me… and it’s hot outside… I’m going to take my pre-shabbat dip.
For a wonderful (hebrew only) source of texts on Parah Adumah go here.
 And ye shall give her unto Eleazar the priest, and she shall be brought forth without the camp, and she shall be slain before his face. And Eleazar the priest shall take of her blood with his finger, and sprinkle of her blood toward the front of the tent of meeting seven times. And the heifer shall be burnt in his sight; her skin, and her flesh, and her blood, with her dung, shall be burnt. And the priest shall take cedar-wood, and hyssop, and scarlet, and cast it into the midst of the burning of the heifer. Then the priest shall wash his clothes, and he shall bathe his flesh in water, and afterward he may come into the camp, and the priest shall be unclean until the even.
וּנְתַתֶּם אֹתָהּ, אֶל-אֶלְעָזָר הַכֹּהֵן; וְהוֹצִיא אֹתָהּ אֶל-מִחוּץ לַמַּחֲנֶה, וְשָׁחַט אֹתָהּ לְפָנָיו.
וְלָקַח אֶלְעָזָר הַכֹּהֵן, מִדָּמָהּ–בְּאֶצְבָּעוֹ; וְהִזָּה אֶל-נֹכַח פְּנֵי אֹהֶל-מוֹעֵד, מִדָּמָהּ–שֶׁבַע פְּעָמִים.
וְשָׂרַף אֶת-הַפָּרָה, לְעֵינָיו: אֶת-עֹרָהּ וְאֶת-בְּשָׂרָהּ וְאֶת-דָּמָהּ, עַל-פִּרְשָׁהּ יִשְׂרֹף.
וְלָקַח הַכֹּהֵן, עֵץ אֶרֶז וְאֵזוֹב–וּשְׁנִי תוֹלָעַת; וְהִשְׁלִיךְ, אֶל-תּוֹךְ שְׂרֵפַת הַפָּרָה
שאל עובד כוכבים אחד את רבן יוחנן בן זכאי: אילין עובדייא דאתון עבדין [הדברים האלה שאתם עושים] נראין כמין כשפים. אתם מביאים פרה, ושורפין אותה, וכותשין אותה, ונוטלין את אפרה, ואחד מכם מטמא למת מזין עליו שתים ושלוש טיפין [=טיפות (של מי הפרה)], ואתם אומרים לו: טהרת