What was the "Urim ve'Tumim"?
), via which Hashem created three hundred and ten worlds (which every Tzadik will merit in the world to Come (See Mishnah at the end of Uktzin), and which is engraved on the Even Shesiyah (the stone on which Hashem founded the world), with which He stopped up the great deep at the time of the creation - and whoever mentions it in time of trouble will be saved (Targum Yonasan).
If the Nochrim are able to divine the future using the powers of Tum'ah, how much more so are Yisrael able to do so using the power of Kedushah; since Hashem created the two powers pitted one against the other (Rashbam).
Why was it called by that name?
Rashi and Targum Yonasan: Because it caused the Choshen to illuminate its message (Urim) and enabled the Kohen Gadol to arrive at the accurate conclusion (Tumim). 1
Ramban: The Urim ve'Tumim 2 comprised two sets of Holy Names of Hashem - one that caused the relevant letters 3 to light-up (Urim); the other, that enabled the Kohen Gadol to read the letters correctly (Tumim), even though they did not necessarily appear in the order that they needed to be read. 4
In the time of the second Beis-ha'Mikdash, the Kohen Gadol wore the Choshen Mishpat because it was one of the eight Begadim that he was Chayav to wear, even through it did not contain the Urim ve'Tumim (whice were hidden together with the Aron ha'Kodesh).
Which constituted a level of prophesy that was lower than Nevu'ah, but higher than the Bas Kol that they employed in the time of the second Beis-ha'Mikdash (Ramban).
That spelled the answer to the questioner (Ramban).
See Ramban, who elaborates.
Why does the Torah insert a 'Hey' at the beginning of "Urim ve'Tumim", even though they have not been mentioned before?
What did Aharon do to merit wearing the Choshen on his heart?
When did Moshe actually place the Urim ve'Tumim inside the Choshen?
Ramban: After he dressed Aharon in the Bigdei Kehunah. 1
What purpose did the stones of the Choshen serve?
Refer to 28:15:1 - 5.
Ramban #1 (Pasuk 35, citing Midrash Rabah): When the Kohen Gadol entered the the Heichal on Yom Kipur, Hashem looked at them and remembered the merits of Yisrael. 1
Ramban (Ibid.): It can be compared to the tutor of the king's son, who wnted to come before the king to plead on behalf of his son, but who was afraid that the king's men wojuld attack him. So what did the king do? He dressed him in his royal robes, thereby causing his men to be afraid to touch him. In the same way, Aharon had to enter the Kodesh Kodshim 2 many times on Yom Kilpr) and these merits (of K'lal Yisrael) entered with - only he was unable to do so, because of the angels who were serving Hashem. 3 Therefore Hashem dressed him in the image of His royal robes, 4