A Commentary, Critical, Practical, and Explanatory on the Old and New Testaments, by Robert Jamieson, A.R. Fausset and David Brown  at sacred-texts.com
num 19:2THE WATER OF SEPARATION. (Num. 19:1-22)
This is the ordinance of the law--an institution of a peculiar nature ordained by law for the purification of sin, and provided at the public expense because it was for the good of the whole community.
Speak unto the children of Israel, that they bring thee a red heifer without spot, &c.--This is the only case in which the color of the victim is specified. It has been supposed the ordinance was designed in opposition to the superstitious notions of the Egyptians. That people never offered a vow but they sacrificed a red bull, the greatest care being taken by their priests in examining whether it possessed the requisite characteristics, and it was an annual offering to Typhon, their evil being. By the choice, both of the sex and the color, provision was made for eradicating from the minds of the Israelites a favorite Egyptian superstition regarding two objects of their animal worship.
num 19:3ye shall give her unto Eleazar the priest that he may bring her forth without the camp--He was the second or deputy high priest, and he was selected for this duty because the execution of it entailed temporary defilement, from which the acting high priest was to be preserved with the greatest care. It was led "forth without the camp," in accordance with the law regarding victims laden with the sins of the people, and thus typical of Christ (Heb 13:12; also Lev 24:14). The priest was to sprinkle the blood "seven times" before--literally, "towards" or "near" the tabernacle, a description which seems to imply either that he carried a portion of the blood in a basin to the door of the tabernacle (Lev 4:17), or that in the act of sprinkling he turned his face towards the sacred edifice, being disqualified through the defiling influence of this operation from approaching close to it. By this attitude he indicated that he was presenting an expiatory sacrifice, for the acceptance of which he hoped, in the grace of God, by looking to the mercy seat. Every part of it was consumed by fire except the blood used in sprinkling, and the ingredients mixed with the ashes were the same as those employed in the sprinkling of lepers (Lev 14:4-7). It was a water of separation--that is, of "sanctification" for the people of Israel.
num 19:7the priest shall be unclean until the even--The ceremonies prescribed show the imperfection of the Levitical priesthood, while they typify the condition of Christ when expiating our sins (Co2 5:21).
num 19:11He that toucheth the dead body of any man shall be unclean--This law is noticed here to show the uses to which the water of separation [Num 19:9] was applied. The case of a death is one; and as in every family which sustained a bereavement the members of the household became defiled, so in an immense population, where instances of mortality and other cases of uncleanness would be daily occurring, the water of separation must have been in constant requisition. To afford the necessary supply of the cleansing mixture, the Jewish writers say that a red heifer was sacrificed every year, and that the ashes, mingled with the sprinkling ingredients, were distributed through all the cities and towns of Israel.
num 19:12He shall purify himself . . . the third day--The necessity of applying the water on the third day is inexplicable on any natural or moral ground; and, therefore, the regulation has been generally supposed to have had a typical reference to the resurrection, on that day, of Christ, by whom His people are sanctified; while the process of ceremonial purification being extended over seven days, was intended to show that sanctification is progressive and incomplete till the arrival of the eternal Sabbath. Every one knowingly and presumptuously neglecting to have himself sprinkled with this water was guilty of an offense which was punished by excommunication.
num 19:14when a man dieth in a tent, &c.--The instances adduced appear very minute and trivial; but important ends, both of a religious and of a sanitary nature, were promoted by carrying the idea of pollution from contact with dead bodies to so great an extent. While it would effectually prevent that Egyptianized race of Israelites imitating the superstitious custom of the Egyptians, who kept in their houses the mummied remains of their ancestors, it ensured a speedy interment to all, thus not only keeping burial places at a distance, but removing from the habitations of the living the corpses of persons who died from infectious disorders, and from the open field the unburied remains of strangers and foreigners who fell in battle.
num 19:21he that sprinkleth . . . ; and he that toucheth the water of separation shall be unclean until even--The opposite effects ascribed to the water of separation--of cleansing one person and defiling another--are very singular, and not capable of very satisfactory explanation. One important lesson, however, was thus taught, that its purifying efficacy was not inherent in itself, but arose from the divine appointment, as in other ordinances of religion, which are effectual means of salvation, not from any virtue in them, or in him that administers them, but solely through the grace of God communicated thereby.