We can find the explanation in the question itself. As mentioned above, Beraysoh is derived from the Aramaic word "outside." On a deeper level, the word "outside" conveys something very positive. We are taking the teachings of the Sages of the Mishnah and transporting them to somewhere seemingly outside the realm of the Torah.
This is a fundamental part of the entire Torah. On the one hand, the Torah is a "secret treasure, which You had hidden... before the world was created." However, the Torah also "descended from its place of glory ... and progressively descended through hidden stages, stage after stage, with the descent of the worlds, until it clothed itself in physical objects and this-worldly things." Despite this tremendous descent, it retains its essence. Even in this corporal, physical world, it remains Hashem's Will and Wisdom. There, it has the power to elevate and refine this world; it can be used to transform this world into "a dwelling place for Hashem below."
We see this idea of the Torah "progressively descending through stages" at the beginning of Pirkei Avos. It tells us that "Moshe received the Torah from (Hashem at Mount) Sinai and gave it to Yehoshua. Yehoshua gave it over to the Elders, the Elders to the Prophets, and the Prophets gave it over to the Men of the Great Assembly." The commentaries explain that the Mishnah is telling us the chain of the Torah's transmission.
