"These are the offspring of Noach, Noach was a righteous man" (Bereishis 6, 9). What is the connection between Noach's offspring and his righteousness? The answer, says Rashi, is that the Torah is informing us that the primary progeny of a person are his righteous deeds. Rashi's explanation still needs further elucidation: Why are one's mitzvos considered his progeny?
Rav Wolbe (Shiurei Chumash) explains the comparison as follows. When raising a child, parents hope and pray that their child will be physically and emotionally healthy. Additionally, when he comes of age, the parents marry off the child so that he, too, can produce another generation, and that generation will produce yet another one. Likewise, when one performs a mitzvah, it should be a "healthy" mitzvah - executed in a manner that achieves its entire purpose, and, when possible, the outcome should last for generations to come.
We beseech Hashem in davening, "So that we not toil for naught" (U'va L'tzion). In other words, we are praying that our actions should achieve the desired results. For example; one might found an organization, along with all that goes into such a massive endeavor, only to find that the officers do not see eye to eye and simply cannot get along with each other. The organization then has elections and votes in new administrators, and they, too, end up fighting, and ultimately the organization falls apart. In such a scenario, all the toil that went into creating the organization was for naught. In contrast, a wise man ponders and deliberates before initiating an action to determine if the intention behind his endeavor is pure, and he anticipates what problems may arise. Finally, when he does act, it is with vigilance and astuteness. He nurtures an action as one would nurture a child. In this vein, we must be careful that our tzedakah is given to worthwhile causes. Giving tzedakah to an unworthy cause is another example of "toiling for naught" (See Bava Basra 9b).
Rav Wolbe adds that there is also a deeper understanding of the Torah's equating mitzvos with progeny. There are those who study Torah as they would any other area of wisdom. They have no specific interest in the Torah being absorbed into their very being, and consequently, such Torah does not become integrated into their personalities. Moreover, it is possible that the Torah will have a negative effect on them, as Chazal tell us (Yoma 72b), "[If] one does not merit [to study the Torah properly] it (the Torah) acts as a poison."One must personally identify with Torah in the same way that he identifies with his children.
A righteous deed has the ability to live on for many generations. This depends to a great extent on the purity of one's intentions and his foresight.