The Lieberman clause is a clause included in a ketubah (Hebrew: כתובה Jewish wedding document), created by and named after Talmudic scholar and Jewish Theological Seminary of America professor Saul Lieberman, that stipulates that divorce will be adjudicated by a modern bet din (rabbinic court) in order to prevent the problem of the agunah, a woman not allowed to remarry religiously because she had never been granted a religious divorce.
Eventually, liberal voices within the Rabbinical Assembly won out, and the movement authorized unilateral action.
In effect, it was an arbitration agreement used in the case of a divorce; if the marriage dissolved and the woman was refused a get from her husband, both the husband and wife were to go to a rabbinic court authorized by the Jewish Theological Seminary of America and heed their directives, which could (and usually did) include ordering a man to give his wife a get.
For that reason, state courts have disagreed in terms of recognition of this clause, in a religious document, in a civilian legal setting.
However, even some Conservative rabbis grew to have misgivings about the religious validity of this approach, eventually leading the joint bet din of the Conservative movement to develop alternative approaches to the problem of the agunah, which include but are not limited to hafka'at kiddushin (Hebrew: הפקעת קידושין), retroactive annulment of the marriage.