29 Thou shalt not delay to offer the first of thy ripe fruits, and of thy liquors: the firstborn of thy sons shalt thou give unto me.
30 Likewise shalt thou do with thine oxen, and with thy sheep: seven days it shall be with his dam; on the eighth day thou shalt give it me.
31 And ye shall be holy men unto me: neither shall ye eat any flesh that is torn of beasts in the field; ye shall cast it to the dogs.
In these laws the people are reminded of their obligation to offer their firsts to the Lord. The first of their fruit, of their liquor, of their oxen and sheep. Even offering the firstborn of their sons as priests.
The general understanding among scholars as to why verse 30 says the firstborn cattle would remain with their mothers for a week is so that they could give their mothers relief by drawing the milk from the udder. It would also allow them to be stable, strong, and clean before being brought to the Lord.
Verse 31 is a quick aside that tells the people that they must not eat carrion. Late on we will hear more on the dietary restrictions of the Mosaic law, but the carcass of even a clean animal would not be fit for human consumption, only for the feeding of one’s dogs. This is, of course, a very practical law, one that would safeguard the Israelites from consuming spoiled or infected meat.