Our Gemara, based on verses, refers to the three sins that require martyrdom—idolatry, murder, and sexual immorality—as tamey, a term usually used to describe something rendered contaminated and no longer at its appropriate level of purity. Tosafos ibid says this is a metaphoric use of the word, but there is no literal and actual impurity rendered by these sins.
But what does the metaphor express? In a Torah mystical view, tamey is the opposite of pure and holy and represents the impingement or disruption of what should be the experience or presence of God. This is why conditions or situations that signal the presence of death and/or the loss of life have tuma: when the ability to connect to God becomes obstructed, the forces of destruction and chaos fill in the blank space. Certain sins drive back connection to God so strongly that they create a vacuum, which unfortunately leads to the space being filled with impurity and destructive forces.
What is interesting is that this is not only taken metaphorically. The Chasam Sofer (Shu”t YD 194) seriously considers the possibility that one who commits one of these three sins may be required to immerse in the mikvah. Additionally, Rama (YD 268) says that it is fitting and proper for a mumar (habitual sinner) who has repented to immerse in the mikvah.
In the modern world, we tend to downplay the impact and expression of symbolic actions. We are influenced by the scientific mindset and believe that objective reality and truth are the most powerful determinants in our lives. While thinking scientifically and looking at cause and effect greatly spurred scientific discoveries of the modern era since the time of Newton, that is only in one realm. In the realm of human experience, our perception and narrative are more impactful than what we like to call objective reality. We are constantly interpreting and experiencing events based on our narrative. As a small example, a confident person who receives a rejection letter thinks, “They were threatened by my ideas, but just as well, I want my writing to appear elsewhere.” Meanwhile, a less confident person who receives a rejection letter thinks, “They saw how bad my writing was. It is obvious that I’ll never be a good writer.”
How we write the narrative impacts our reality, which is formed much less by facts and more by the emotions and relationships that are activated. This is why symbolic acts, such as wailing through the trumps of the shofar, eating in booths on Succos, or refraining from leavened bread on Passover, are ways of internalizing and creating states of thought and emotion. It is no small thing to immerse in the primordial waters and feel oneself cleansed and reborn. This act is an expression and enactment of our wish to start fresh, becomes a theurgic prayer through action, and creates a new reality within us.
Translations Courtesy of Sefaria, except when, sometimes, I disagree with the translation 
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Rabbi Simcha Feuerman, Rabbi Simcha Feuerman, LCSW-R, DHL is a psychotherapist who works with high conflict couples and families. He can be reached via email at simchafeuerman@gmail.com