The term “ta’amei ha-mitzvot” literally translates as “reasons for the commandments.” The question “why should we do mitzvot” is easy to misunderstand. Many simply reply “because God said so”, which, even if correct, merely prompts the question, “why did God say so.” To answer that second question with “just because” or “no reason” renders God’s will arbitrary and thus, lacking justification.
The question should properly be broken down into two related but distinct questions: (1) why did God command us? and (2) why should we follow that command? As to the first question, the Mishnah (Makkot 3:16) is clear: “The Holy One, blessed be He, desired to grant merit to Israel. Therefore, he proscribed for them Torah and mitzvot.” As Rabbi Pinchas Kehati explains (summarizing the gemara’s commentary on this mishnah): “He multiplied warnings and prohibitions for them, even regarding things from which man naturally keeps apart, for since they stay away from them because the Torah has thus commanded, their merit is increased.” There are two important implications here. One, the proscribed deeds have some merit to begin with. They are justified, at least in part, without the divine imperative. Two, the addition of the divine command somehow enhances the already-righteous deeds.
I think Rabbi Louis Jacobs captures this idea well (“The Relationship Between Religion and Ethics in Jewish Thought”):
Although God commands them it is not implied that the command is the reason for their observance, so that if God had commanded man to steal or to murder this would have been the right thing to do. On the contrary, the commands are announced in such a way as to suggest that they are already fully comprehensible to man as the basis for living the ethical life. . . . Once God has commanded, however, the command itself is, of course, an additional reason for its observance.
As to the second question (why should we follow God’s command), there is a tension between acting because God commanded and acting because of whatever reason God commanded. The Maharal of Prague, in his Tifferet Yisra’el, suggests that “the man of true piety” embraces both elements. Rabbi Marvin Fox (“The Moral Philosophy of MaHaRal”) paraphrases the Maharal’s position as follows:
[W]hatever is divinely commanded through the Torah is intrinsically good. The social utility or wide-spread general acceptance of particular commandments may add to their attractiveness from our limited human perspective. Their ultimate ground, however, is their intrinsic value. Since we are incapable of grasping this fully through our own resources, we submit in modest awareness of our creaturely finitude to the divine wisdom. . . . We have here two poles of a dialectical exposition. On the one hand, virtues are conceived as divine decrees to which man can only submit in faithful self-suppression. On the other hand, virtues are conceived as intrinsically valuable and thus commanding the freely given assent of any intelligent person. Thesis and antithesis are synthesized in the actual situation of man. The very process of submission grants him the illumination which in turn leaves no doubt about the intrinsic worth of the commandments. Thus, the man of true piety will observe the commandments with a combination of loyalty to God’s word and intelligent apprehension of the supreme wisdom implicit in that word.