11 And it shall be when the Lord shall bring thee into the land of the Canaanites, as he sware unto thee and to thy fathers, and shall give it thee,

12 That thou shalt set apart unto the Lord all that openeth the matrix, and every firstling that cometh of a beast which thou hast; the males shall be the Lord’s.

13 And every firstling of an ass thou shalt redeem with a lamb; and if thou wilt not redeem it, then thou shalt break his neck: and all the firstborn of man among thy children shalt thou redeem.

Obviously Israel departing Egypt and marching to Canaan was a fulfillment the promise God made to Abraham. But as verse 11 points out, it was not only a promise to Abraham. Moses told the Israelites “the Lord shall bring thee into the land of the Canaanites, as he sware UNTO THEE and to thy fathers. God had promised the land of Canaan anew to all of the people of Israel that lived in that day. In fact, if anything, the promise was more to them than to Abraham, as Abraham would only receive it through them.

And in return for God giving this gift to His people, the people were again reminded of how they must consecrate their firstborn to the Lord. “All that openeth the matrix” means the first child that breaches the walls of its mother’s womb. Though again, it was specifically to be the firstborn male. It is unclear to me if the firstborn was a female, whether the first male born thereafter would still be taken and consecrated to the Lord, or if there would be no consecration from that family unit, since the first male would not have “opened the matrix.”

Also, note that it was only clean beasts that were meant to be given as an offering, which is why the firstling donkeys were not eligible. A clean lamb could be given in its place, presumably a lamb that was not already owed to the Lord by being a firstborn, or if the person refused to give a lamb or had none to give, the donkey would be put to death, as then no one would have a claim on it.