It is religious life.
A beit midrash, literally a house of study, is the Jewish space devoted to learning Torah and related texts. It may exist inside a synagogue, yeshiva, school, or communal building, but its defining purpose is not prayer first. It is study: questioning, arguing, reading, teaching, and sitting inside texts with other people.
A beit midrash is not exactly the same thing as a synagogue
Chabad's overview makes the distinction directly. A beit knesset is primarily a house of prayer. A beit midrash is oriented toward study. The two may share one building, and often do, but they are not conceptually identical.
That difference matters because Judaism has long given learning its own institutional dignity.
The beit midrash is not just a classroom. It is a place where texts are worked through as a communal discipline and, in many traditions, as a sacred act.
The culture of the beit midrash is dialogical
My Jewish Learning's discussion of Torah study describes the beit midrash as the classic setting for the give-and-take of Jewish learning. Students do not merely absorb information. They question, compare, argue, and interpret.
That is one reason the beit midrash occupies such a central place in Jewish intellectual life. It protects a style of learning that assumes truth is sharpened through conversation rather than passive reception.