Jamieson, Fausset and Brown on Exodus 28:30

30. thou shalt put in the breastplate of judgment the Urim and Thummim--The words signify "lights" and "perfections"; and nothing more is meant than the precious stones of the breastplate already described (compare Ex 39:8-21; Le 8:8). They received the name because the bearing of them qualified the high priest to consult the divine oracle on all public or national emergencies, by going into the holy place--standing close before the veil and putting his hand upon the Urim and Thummim, he conveyed a petition from the people and asked counsel of God, who, as the Sovereign of Israel, gave response from the midst of His glory. Little, however, is known about them. But it may be remarked that Egyptian judges wore on the breast of their official robes a representation of Justice, and the high priest in Israel long officiated also as a judge; so that some think the Urim and Thummim had a reference to his judicial functions.