The Mizan is the balance set up on the Day of Resurrection. "We shall set up the scales of justice for the Day of Resurrection, so that no soul will be dealt with unjustly in the least" (21:47); those whose scales are heavy prosper, and those whose scales are light have lost themselves (7:8-9, 23:102-103, 101:6-9). The image is one of the fixed furnishings of Qur'anic eschatology, standing alongside the trumpet, the record given into the right or left hand, and the bridge.
The same word does other work in the Qur'an. God "raised the heaven and set up the balance" (55:7), and the passage moves immediately to a command not to cheat in weighing (55:8-9), as it does again in the denunciation of those who give short measure (83:1-3). Justice in the marketplace and justice at the judgement are named by one word, which is why Muslim ethical writing has treated commercial honesty as a directly theological matter rather than a merely civil one.
How the weighing works was debated. Traditionist and Ash'ari theologians generally affirmed a real balance, differing over whether what is weighed is the deeds themselves, the scrolls recording them, or the agent; Mu'tazili and later rationalist readings took the scales as a figure for perfectly exact justice, since acts are not the kind of thing that has weight. Historians of religion note that a weighing at judgement recurs in Egyptian funerary texts and in Zoroastrian material; whether that reflects transmission or the independent reach of an obvious metaphor for exactness is not settled.