"Speak to the children of Israel that they bring you a red heifer, a perfect one, in which there is no blemish, on which no yoke ever came." (Numbers 19:2, HBFV throughout)
The heifer colored red was to be burned completely by fire and its ashes collected and stored "for the congregation of the children of Israel for the water of purification; it is for purifying from sin" (Numbers 19:9). The ashes were then placed in a container where running water was put on them (verse 17). The mixture was then used by the priest.
What makes the ceremony in Numbers 19 special (other than in the use of a red heifer) is that it is the only one in the Old Testament where blood is burned for a ceremonial purpose. In fact, the entire animal (including the fecal matter in its body) is consumed by fire (verse 5). The use of the ashes of a heifer, as an integral part of a temple-sanctioned event, also makes this service unique.
Both those born in the land of Israel and those who are 'strangers' (aliens or Gentiles living in the land) could participate in the Numbers 19 ceremony involving this special heifer (Numbers 15:14 - 15). Additionally, as no provision was made for sending its ashes to different locations, this purification ceremony could only be participated in by those who came to Jerusalem's temple.
Why are ashes needed?
Ashes of a heifer colored red are needed so that they, with running water, can create what is translated as 'water of purification' (NKJV), ''water of cleansing' (HBFV, NIV), 'water of separation' (KJV), 'water to remove impurity' (NASB), 'water for the purification' (NLT) and 'waters of separation' (YLT). The word translated as purification, cleansing, separation, etc. in these verses is niddah (Strong's Concordance #H5079) which in the Hebrew means rejection and by implication impurity.
The purpose of this ceremony is to purify, ceremonially, those who are unclean. It was primarily used to cleanse those who were exposed to a dead body (Numbers 19:11, 13). It was also used to remove ritual defilement created by taking booty from a war.
In the Jewish Mishna (Parah 3:2) it states that children were sent to the pool of Siloam to collect water for the red heifer ceremony. They traveled to and from the pool, on the back of bulls, so that they could remain unpolluted by not touching the ground.
An early Jewish tradition believed that the Numbers 19 ceremony was implemented to atone for Israel's sin of worshipping a golden calf. This incident (Exodus 32), which occurred as the children of Israel waited for Moses to come down from Mount Sinai, angered God to the point where he wanted to DESTROY all the people (Exodus 32:7 - 10). Their behavior not only caused Moses to break the stone tablets containing the Ten Commandments, but also to have the idolatrous calf ground into powder and poured into water that the sinning Israelites had to drink (Exodus 32:20).
Another tradition holds that Solomon's God-given wisdom was able to help him understand all things EXCEPT the meaning of the red heifer. The command in Numbers 19 states that an animal must be selected "on which a yoke has never come" (verse 2). Yet, in another example of going way beyond God's intent in order to create human traditions (see Matthew 15, Mark 7), the Mishna states that even a cloth placed on the animal, such as a heifer, would be considered a 'yoke' and render it unfit for use in the ceremony.
The New Testament
It is believed that the waters from the pool of Siloam, the same place where Jesus healed a man born blind, were used to combine with the ashes of a red colored heifer to create what was needed to make someone ceremonially clean (see John 9:1 - 7). The apostle Paul references this animal in the book of Hebrews. He emphatically informs us that the ashes of the animal could never purify our consciences before God. Only the blood of Christ, which makes our forgiveness possible, can perform that monumental task (see Hebrews 9).
There have been no animal sacrifices in Jerusalem since the Roman Empire destroyed the temple in 70 A.D. Some modern orthodox Jews, however, look for a time when daily animal sacrifices can be establishing again in Jerusalem on an altar that will first be cleansed by the ashes of a heifer colored red. Towards this end, some Rabbis are on a continuing quest to find such an unblemished animal. The fact that some kind of altar and temple will be erected and used in the End Time before Christ's return has been predicted (Mark 13:14, Matthew 24:15, 2Thessalonians 2:3 - 4).