The Reformation slogan is often heard as a claim that nothing but the Bible has any standing. That is not what the Reformers argued, and the difference matters.
Their claim was about norms. Scripture is the final court: every other authority, whether council, pope, bishop, tradition or private conviction, is answerable to it and correctable by it. Luther's statement at Worms in 1521, that he could not recant unless convinced by Scripture or plain reason because popes and councils have contradicted one another, is the position in its native form. It is a claim about which authority is ultimate when authorities conflict.
That left plenty of room for the rest. The Reformers used the ecumenical creeds, wrote confessions and catechisms and required subscription to them, quoted the church fathers constantly, and expected ordinary Christians to be taught rather than to work it out alone. Lutheran and Reformed churches promptly built confessional structures more detailed than anything medieval Catholicism had imposed on the laity. Theologians distinguish this classical position, sometimes labelled the norming norm above the normed norms, from the later view that the Bible functions alone in the hands of the individual reader with no interpretive community at all. That stronger position, sometimes called solo scriptura to mark the difference, belongs to eighteenth and nineteenth-century restorationist and revivalist movements and is now widespread in independent evangelicalism.
Supporting the principle are two further Reformation claims: the perspicuity of Scripture, that what is necessary for salvation is clear enough to be grasped by an ordinary reader, and the sufficiency of Scripture, that it contains what is needed and nothing further need be revealed. Both were arguments for translation and for putting the text in lay hands, which is the practical legacy the principle is remembered by.