After Bnei Yisrael are commanded (reminded) not to consume the blood of an animal, Moshe provides a strong incentive to listen:
The nature of a father (parent), flows into and can get passed down to children. Therefore, the Torah says that avoiding blood will be “good for you and for your children after you” so that the terrible trait of cruelty does not flow from you into future generations.
The full section inside:
‘כו רַק קָדָשֶׁיךָ אֲשֶׁר יִהְיוּ לְךָ וּנְדָרֶיךָ תִּשָּׂא וּבָאתָ אֶל הַמָּקוֹם אֲשֶׁר יִבְחַר ה
כז וְעָשִׂיתָ עֹלֹתֶיךָ הַבָּשָׂר וְהַדָּם עַל מִזְבַּח ה אֱ-לֹ-הֶיךָ וְדַם זְבָחֶיךָ יִשָּׁפֵךְ עַל מִזְבַּח ה’ אֱ-לֹ-הֶיךָ, וְהַבָּשָׂר תֹּאכֵל
כח שְׁמֹר וְשָׁמַעְתָּ אֵת כָּל הַדְּבָרִים הָאֵלֶּה אֲשֶׁר אָנֹכִי מְצַוֶּךָּ לְמַעַן יִיטַב לְךָ וּלְבָנֶיךָ אַחֲרֶיךָ עַד עוֹלָם כִּי תַעֲשֶׂה הַטּוֹב וְהַיָּשָׁר בְּעֵינֵי ה’ אֱ-לֹ-הֶיךָ
Perhaps somewhat allegorically, the Torah is highlighting the importance of the examples that parents set for their children. A parent’s tremendous influence can either have incredibly positive or disastrously negative outcomes. If a parent has cruel traits – whether it be from literally consuming blood (unlikely these days) or simply not keeping his/her anger and emotions in check – then, as the Kli Yakar notes, that can easily, and tragically, be passed down to a child, whether intentionally or not. Assuring that we don’t have such traits will be good for us and for our children
On the flip side, if a parent has the traits of loving Hashem and demonstrating thanks to Hashem for all the good He has provided, then that example will hopefully be seen and emulated by that parent’s children. The root of the Hebrew word for sacrifice – korban – is ק.ר.ב. , which means ‘close/near’. The closeness that a parent strives to achieve with Hashem and cherishes with Hashem, will hopefully be a path adopted by the child, bringing richness and goodness to the parent, child and future generations to come.