Deeds of the Avos reach all generations

המאכלת דרשו חז"ל שבנ"י אוכלין מתן שכרה.

The "ma'acheles" (knife) - Chazal expounded that Bnei Yisrael "eat" the reward given for it.

On the word "ma'acheles," the knife Avraham took at the Akeidah, Chazal play on its root (related to "eating") to teach that Bnei Yisrael partake of - "eat" - the reward generated by Avraham's act. The Sefas Emes will explain how the merit of one deed nourishes future generations.

וכתוב ויקח שאברהם אבינו ידע זה שכל מעשיו הם עצות עבור כלל ישראל שהוא אב לכולם וכן צריך כל אדם להתבונן כי מעשיו נוגעין לדורי דורות.

And it is written "vayikach" (and he took) - that Avraham Avinu knew this, that all his deeds are designs for the sake of Klal Yisrael, for he is the father of them all; and so too every person must contemplate that his deeds affect generations upon generations.

The word "vayikach" (Avraham "took" the knife) shows his awareness that his every act was being performed on behalf of the entire nation, since he is the father of all Bnei Yisrael. From this each person should reflect that his own actions, too, reach far beyond himself and influence countless future generations.

ועי"ז אוכלין בנ"י מתן שכרה ע"י שהם עזרו להאבות למעשיהם הטובים כי בודאי כח האבות הי' ע"י שכל שורש בנ"י היו בתוכם והכל במשפט אמת כנ"ל:

And through this Bnei Yisrael "eat" the reward given for it, since they themselves helped the Avos in their good deeds - for surely the power of the Avos came about through the fact that the entire root of Bnei Yisrael was within them, and all is by true justice, as above.

Bnei Yisrael are able to partake of the reward of Avraham's act because, in a real sense, they participated in it: the very root and souls of all future Jews were already contained within the Avos. The Avos drew their strength from carrying that entire nation within them, so it is perfectly just ("mishpat emes") that their descendants share in the reward of deeds they were, at their root, part of.

Summary: The knife of the Akeidah teaches that Bnei Yisrael "eat" the reward of Avraham's deed because the souls of all future Jews were already rooted within the Avos and thus shared in their good deeds; from this every person should recognize that his own actions, like Avraham's, ripple through generations - and that it is true divine justice for descendants to partake of merits they were, at their root, part of.