Urin and Thummin: both the Hebrew words and the exact nature of the objects so designated are uncertain. They were apparently lots of some kind which were drawn or cast by the priest to ascertain God’s decision in doubtful matters. Hence, the burse in which they were kept was called “the breastplate of decision.”
The Urrim V’Tummim was another name for the breastplate of the high priest. The plate had a set of precious stones with the names of the tribes on it. When the people wanted an answer from G-d, the stones would “light up” in an certain order and if the high priest was worthy of “divine inspiration” he would be able to decipher the message. This is the standard jewish traditional understanding of the Urrim V’Tummim. There is no reference anywhere to lots of any kind. It also explains why it is always the high priest doing the ceremony.
TQMshirt has it pretty much down, except that the “Urim and Thummim” were something that was placed inside a pocket of the breastplate, not an alternate name for the breastplate itself. Jewish commentaries are uncertain as to what they were, but the main speculation is that it referred to scripts of the holy name of G-d written in a special, mystical way.
And also, the letters would light up, but not in order. It was up to the High Priest to decipher the message properly.