Shiurim in this topic
This phrase refers to a principle in Talmudic law. When there is a disagreement between the schools of Beit Shammai and Beit Hillel, Jewish law almost always follows the opinion of Beit Hillel. The phrase means that if a teaching is recorded in line with Beit Shammai's opinion instead of Beit Hillel's, it does not carry the authority of a "Mishnah." In other words, such a ruling is not considered binding because the halacha (law) follows Beit Hillel.
This reflects the broader principle that Beit Hillel's opinions were usually accepted as the final law in rabbinic tradition. Therefore, a ruling following Beit Shammai in place of Beit Hillel has no halachic validity.