“And in the eighth day the flesh of his foreskin shall be circumcised.”
At the stage in fact when this law was first communicated, circumcision could not take place. It would have been unwise while constantly on the move. The instructions were thus in the final analysis for when they settled in the land. They were in the light of the soon anticipated entry into Canaan. (These instructions may have been given prior to the disobedience that cancelled that entry, thus with its full application being delayed, or it may have been shortly before Moses' death, and used as an incentive to press the people to go forward).
Looked at in practical terms the seven days would also be necessary because time had to be given to her for recovery before she attended at the circumcision of a male child (see Genesis 17:10-14; Genesis 21:4). While circumcision was mainly seen as the father's responsibility, unless he was too ill for it (Exodus 4:24-26), God graciously provided so that the woman could be fit enough to be present. He was her son too.
The circumcision would be performed, usually by the father, using a flint knife, by removing the foreskin. It was the shedding of covenant blood to seal the child in the covenant. It is probable that it was also seen as acting as a kind of blood offering, declaring the redemption of the child, and thus lessening the time needed for recovery in the case of a male child. They would have noticed that discharges of lochia did not occur for so long a period in the case of a male child.
The use of a flint knife for circumcision, following ancient tradition (see Exodus 4:25), was in fact much safer than using a metal knife, for the flint was naturally sterilised. It is also an interesting medical fact that the eighth day was probably the best and most painless period after birth for carrying out this operation. Up to about the fifth day the newborn babe was susceptible to haemorrhage, later the nerves would have become more sensitive.
Circumcision was a sign of the covenant that God made with Abraham in Genesis 17. Every male child who was to be seen as a true born Israelite had to be circumcised, and by it he became a member of the covenant people. It was also open to ‘strangers' who wished to eventually become ‘true born Israelites' (Exodus 12:48). But it was not carried out during the travels in the wilderness, presumably precisely because they were travelling, and it would be inconvenient, and then because of the breach with God which resulted in the stay at the oases around Kadesh. In one sense the covenant was seen as pending.
This non circumcision of the people may have been significant even though it is never explained, especially as it continued in the long period at Kadesh. It would seem that it was linked with the future hope. At first it was probably practical. Circumcision could be tricky while on the move. But it then probably became theological. They would be circumcised once they entered the land of Promise. And until that they were not worthy. The covenant was temporarily partly in suspense until contempt had been purged by the dying out of those who had refused to obey God's command to enter the land (Numbers 14).
All the people who entered the Promised Land who had not been circumcised in Egypt (including the mixed multitude of Exodus 12:38) would in fact be circumcised on reaching it (Joshua 5:2-9). And the blood that was shed in the act of circumcision would almost certainly have been seen in sacrificial terms as making atonement. It was certainly seen as vital for a servant of God (compare Exodus 4:24-26). And from that day on these provisions would apply at every birth.
So the childbearer was through this law of uncleanness going through a repeat of the curse. And that is why sacrifices would have to be offered. Then God would normally give back to her the gift of life, and she would be clean, and her ordeal would be over. So was it indicated that in every birth a sinner was born, affected by the fall, and so was it revealed that he/she would be graciously received by God and be made ‘clean', restored to the state intended for God's people. And so would it also be revealed that she was delivered by God in her childbearing (compare 1 Timothy 2:15).