Parah Adumah is synonymous with the word “Chohk”- a law.
The classic definition of a chohk is a mitzvah that we don’t understand or don’t fully understand it. Whether we don't understand the rational behind it, or we don’t understand how it works, for example the Parah Adumah purifies those that are sprinkled with it, yet at the same time it renders impure those that deal with it- a seemingly sound contradiction.
Whatever the reason is, a chohk is classically understood as something we do, despite the fact we don’t understand what we are doing.
A chohk seems to be hiding something, however, if we look at it from a different angle we will actually see that a chohk actually reveals something very fundamental about the Torah.
There are many reasons and rational as to why we perform certain Mitzvos. In fact, throughout the generations numerous works have been produced to explain and give rhyme and reason to many of the Mitzvos we perform. To list a mere few, the Chinuch, part of the Rambams Moreh Nevuchim, Kuzari, Ramban on the Torah, among many others.
Despite all the "reasons" given, the truth of the matter is, reasons and logic are not why we perform Mitzvos.
The Mishnah in Brachos tells us that if one says in his Tefillos that Hashem is merciful therefore he commanded us to send away the mother bird when we perform the MItzvah of Shiluach haken-we silence that person. The Gemara (Brachos 33) explains (according to one opinion) that what this person is saying, is that Hashem commanded this action for the sake of Mercy on the mother bird, but the truth is the Mitzvot were given to us as commands that we must adhere to- regardless of any mercy.
R' Shamshon Refael Hirsch in his monumental work “Chorev”, sums up this idea very well. Despite the fact that one of the sefers main focuses is Tamei Hametzvos, namely the giving of reasons and rational to the Mitzvos, he says that the ultimate and ONLY answer to the question of "why we do certain things and refrain from others ? Is because Hashem commanded us so, and we must heed his word with all our might.
He further explains that all the reasons and rational can teach us lessons, insights and concepts but they are in no way the reason why we perform the Mitzvos.
The one and only reason is Because Hashem commanded us.
The typical meaning for “Tamei Hamitzvos” is “reasons” for the Mitzvos, however, “Tam” can also mean “Taste” meaning the reasons that give flavor so to speak to the Mitzvos. When something tastes good we engage it whole-heartedly.
When we understand what we are doing we infuse the Mitzvah with flavor, hence we will carry it out with more motivation, accuracy, care and many other positive feelings and emotions.
In realty, many of the Mitzvos we perform can seem like the motivation behind them is the rational and logical explanation. Normal civilized people don’t go around committing murder, most people will claim that it’s immoral and it will destroy society. Stealing as well, your average person refrains from stealing, but as to the reason of their behavior; most people will say that it’s unethical and if people will steal, society would totally disintegrate and the world would be a chaotic place.
Although these reasons are sound and logical, they are not the reasons that Jews don’t murder and steal.
Jews refrain from these despicable actions because Hashem commanded us to refrain from them. Obviously the more of Tamei Hamitzvos (reasons) we have the better we will perform the Mitzvos, that is human nature, but the ultimate reason is because we were commanded.
When we perform a "Chohk" something that seemingly has no reason or rhyme we are demonstrating that we do what Hashem commands us to do whether we understand it or not.
This is a declaration for everything that we do, including the so called "logical Mitzvos". Just as the “Chohk” is done only because Hashem commanded us to do it, so too, the rest of the so called “logical/rational MItzvos” they are performed because Hashem commanded us to perform them.
Thus, the “Chohk reveals that everything we do, each and every Mitzvah we perform and each and every Aveirah we refrain from doing, is only because Hashem commanded us.