Question: What exactly is the Red Heifer Prophecy? How does it relate to today and the end of time?
Response: The "Red Heifer" issue is one that has been much in the news as far as many who are fixated on the end times is concerned. This is largely because of a great many books and articles which have been written on the subject, and because of a report of a "red heifer" which had been born in Israel several years ago.
Let me see if I can clarify this issue from a biblical point of view:
1) There is no "red heifer prophecy" per se, at least not as far as the Bible is concerned. Numbers chapter 19 gives the regulations for the preparation of the Mosaic Law's "waters of purification", requiring the ashes of a suitable and suitably prepared red heifer in order to be appropriate. Nothing here of a prophecy. Also, nothing of any of this in the New Testament (on Heb.9 see below). This issue is dealt with in great detail in the Mishnah (the Jewish commentary on the Law which forms the text to which the Talmuds are in turn commentary), a whole "tractate" in fact, and I am not aware of any prophecy therein either (that is, in the Mishnah, I cannot speak for the Talmuds). Not that any prophecy in extra-biblical Jewish literature would mean anything from the standpoint of biblical prophecy - God's prophetic words for believers are contained only in the Bible.
2) I believe the thinking about the importance of the red heifer in the minds of many who are concerned about the development of end times events is as follows: in order for some of the biblical prophecies to take place, there has to be a reconstructed temple (Rev.11, for instance, clearly mentions a temple and an altar in the Tribulation, and the beast sets up his statue therein, representing himself "as God": 2Thes.2:4). In order for there to be a new temple, so the argument goes, the entire site would first have to be purified (cf. the purifications of Solomon and Hezekiah: 2Chron.2:4; 29:18; but contrast the dedication of the second temple with no specific mention of purification: Ezra 6:14-16). This means that the Rabbins would have to have appropriate water of purification, which means, so this line of thought goes, that they would have to have a red heifer to make it.
3) There is also a lot of talk about "where the ashes of the last red heifer were hidden" at the time of the Romans' destruction of Jerusalem in A.D. 70, but it seems pretty clear that the chances of finding this actual stash of ashes (as opposed to something someone claims is the real thing) is remote indeed. After the Bar Kochba revolt was crushed in the second century, Rome deliberately leveled Jerusalem and placed a Roman colony on the site. All this makes the utilization of a "new" red heifer a more likely thing for those who feel it necessary to get on with temple reconstruction in this way. All this sounds remarkable like the holy grail in many respects, and there are similarities, at least in the sense that neither legend is scripturally important.
4) The important thing to remember in all this is that the Mosaic sacrifices were abrogated by the death of Christ (who fulfilled them by His death), so that no one who "keeps crucifying the Son of God afresh and exposing Him to open shame" can be in the will of God in any way (Heb.6:6 : i.e., to continue participation in the rites which looked forward to Christ's death and therefore by necessity after the fact suggest that He has not yet died for us is something true Christians must have no part in). As Paul says in Hebrews, specifically referencing the cleansing of the red heifer as an earthly rite is in no way to be compared to the cleansing sacrifice of Christ, "For if the blood of goats and bulls, and the ashes of the [red] heifer sprinkled on those unclean sanctify as far as the cleansing of the flesh is concerned, how much more then will the blood of Christ, who offered Himself through the Holy Spirit blameless [i.e., like the heifer] to God cleanse our conscience from dead works to serve the living God!" (Heb.9:13-14).
5) Also, the procedures for the inauguration of the tribulational-millennial temple are actually outlined in Ezekiel 40:18ff., and there is no mention there of the red heifer or the water of purification.
6) So I believe the "bottom line" to all this is that religious (and unbelieving) Jewish clerics and conservatives may indeed be looking for a red heifer and feel this an essential step in the process of reconstructing the temple and re-instituting the temple rite. I have no idea how common or uncommon an event the birth of a young red cow is. At some point, sacrifice of such a heifer to produce the ashes for the water of purification may take place. At some point, said water may be used to purify the temple mount or portions thereof. At some point (and scripture would indicate that this step, at least, is imminent), a third temple will be built. But all of these steps will be taken not as part of the true worship of God. For God may only be truly worshiped now through His Son, our Lord Jesus Christ. The one exception to this is that during the Tribulation, Moses and Elijah, the two witnesses, will reconstitute the temple worship in a correct and godly way as part of their special ministry of Jewish revival (please see the link, in Coming Tribulation part 3A: "The Two Witnesses").
So from a biblical point of view, whether the religious authorities of Israel go through the red heifer mechanics or not to build the (prophesied) temple, and whether or not they do so in a "correct" way is of no great importance in the fulfillment of biblical prophecy beyond the fact that scruples over this issue may be a factor in the delay of these events actually coming to fruition. For more on the actual development of end time events, please see the following two series:
Coming Tribulation: A History of the Apocalypse
The Satanic Rebellion: Background to the Tribulation
Finally, please also see the link, "The Red Heifer and the Millennial Temple".
Hope this gets to your question.
Yours in Christ,