Tsorekha Gevoha: Jewish Theurgy in Kabbalah
[For healing, apply mitzvot here - repeat as necessary. Illustration from Illan Gadol]
The TaNaKH is fickle about explaining the purpose of commandments. Sometimes an explanation of an individual command is offered (why for example, taking bribes is forbidden), sometimes the reason approaches the self-evident (why we shouldn't murder), but often, no explanation for a particular commandment is forthcoming at all (much of the sacrificial system, for example, is mandated without any clear rationale).
The Rabbis attempt to explain the rationale for many of the mitzvot, but again, there is not a lot of effort to offer a systemic theory of the mitzvot, except perhaps this: "Israel is beloved by God, for He surrounded them with mitzvot: tefillin upon their heads and arms, tzitzit upon their garments…This can be compared to a king of flesh and blood who said to his wife: 'Adorn yourself with all your jewelry [I gave you] so that you will be desirable to me” So too the Holy Blessed One says to Israel, “Distinguish yourself with mitzvot so you will be desirable to me.” (Sifrei Deut. 36) In other words, the Rabbis include the mitzvot in their erotic theology: In love God gives us the commandments as ornaments of His love. When Israel wears (performs) them, it enhances God's desire for us.
The rationalists, who generally assume God's impassiblity (God is not subject to human influence) regard the commandments to be entirely for our benefit - they mold us into virtuous people, maintain our social and unique identity, etc. Maimonides is the apotheosis of this approach. Moreover, RaMBaM believes that the rationale for every commandment is discernable. If we can't come up with a logical moral, social, or intellectual purpose for a particular commandment, we simply haven't applied enough brain power to the question. This is the attitude toward the commandments that gives birth to the 'hygiene' theory of kashrut - we separate meat from milk to make better distribution of available proteins, or we don't eat pork, shellfish, etc, because we intuit that these food contain harmful substances.
The early mystics found such rationalizations troubling, because once you figure out how to address the 'rationale" (i.e., cook your pork thoroughly and render it safe), the commandment loses its force. And they were all about keeping the fabric of the commandments a whole cloth. So they made an entirely different argument. No only is God subject to human influence, there is atserokha gevoha - 'a need on high.' The mitzvot don't just help us, they help God. This is baldly stated in the 13th Century mystical treatise Sha'arei Orah, Gates of Light, when Joseph Gilkatilla, the author, asks rhetorically, "Doesn't one see that the lower worlds have power to build or destroy the worlds above?"
This is grabbing the other end of the stick from the radically transcendent and immutable God of much rationalist philosophy. But, rational or not, what this does, religiously, is make the commandments really compelling. It is the cosmic equivalent of Jewish mother's guilt: "So, if you don't do what I ask, it's not like the world's going to come to an end....except it will!" "Go ahead, don't worry about Me, I'm only your Creator!" Thus in Sefer Bahir we read: We learned: There is a single pillar extending from heaven to earth, and its name is Righteous (Tzadik). [This pillar] is named after the righteous. When there are righteous people in the world, then it becomes strong, and when there are not, it becomes weak. It supports the entire world, as it is written, "And Righteousness is the foundation of the world." If it becomes weak, then the world cannot endure. Therefore, even if there is only one righteous person in the world, it is he who supports the world. It is therefore written, "And a righteous one is the foundation of the world."  This logic of sustaining and healing God through righteous deeds creates great incentive for zealous, precise, even exuberant observance. On the other hand, it somewhat stifles innovation (change may diminish the potency of the ritual act) and create a certain degree of religious OCD.
1. Gates of Light, Avi Weinstein, trans. (Harper-Collins, 1994), p. 62.