Notes on the Bible, by Albert Barnes, [1834], at sacred-texts.com
The principle that death and all pertaining to it, as being the manifestation and result of sin Gen 2:17, are defiling, and so lead to interruption of the living relationship between God and His people, is not now introduced for the first time, nor is it at all peculiar to the Mosaic law. It was, on the contrary, traditional among the Israelites from the earliest times, it is assumed in various enactments made already (compare Num 5:2; Num 9:6 ff; Lev 10:1, Lev 10:7; Lev 11:8, Lev 11:11, Lev 11:24; Lev 21:1 ff), and it is traceable in various forms among many nations, both ancient and modern. Moses adopted, here as elsewhere, existing and ancient customs, with significant additions, as helps in the spiritual education of his people.
The ordinance was probably given at this time because the plague which happened Num 16:46-50 about the matter of Korah had spread the defilement of death so widely through the camp as to seem to require some special measures of purification, more particularly as the deaths through it were in an extraordinary manner the penalty of sin.
A red heifer - Red, in order to shadow forth man's earthly body, even as the name Adam bears allusion to the red earth of which man's body was fashioned.
Without spot, wherein is no blemish - As with sin-offerings generally Lev 4:3.
Upon which never came yoke - So here and elsewhere (see the marginal references), in the case of female victims.
The work would necessarily require a priest; yet as it rendered him unclean for the day Num 19:22, the high priest was relieved from performing it.
Without the camp - The defilement was viewed as transferred to the victim that was to be offered for its removal. Under these circumstances the victim, like the defiled persons themselves, would be removed outside the camp. The particular pollution to be remedied by this ordinance was the indirect one resulting from contact with tokens and manifestations of sin, not the direct and personal one arising from actual commission of sin. So too the sinless antitype had to bear the reproach of associating with sinners Luk 5:30; Luk 15:2. And as the red heifer was expelled from the precincts of the camp, so was the Saviour cut off in no small measure during His Life from the fellowship of the chief representatives of the theocracy, and put to death outside Jerusalem between two thieves. Compare Heb 13:11-12.
Compare Lev 14:4 note.
Water of separation - In Num 8:7, the water of purification from sin is the "water of purifying." So that which was to remedy a state of legal separation is here called "water of separation."
He that gathered the ashes became equally unclean with the others. For the defilement of the people, previously transferred to the heifer, was regarded as concentrated in the ashes.
One practical effect of attaching defilement to a dead body, and to all that touched it, etc., would be to insure early burial, and to correct a practice not uncommon in the East, of leaving the deal to be devoured by the wild beasts.