Daniel 5:1,5-6,13,16-31  King Belshazzar made a great feast for a thousand of his lords and drank wine in front of the thousand. … 5 Immediately the fingers of a human hand appeared and wrote on the plaster of the wall of the king’s palace, opposite the lampstand. And the king saw the hand as it wrote. 6 Then the king’s color changed, and his thoughts alarmed him; his limbs gave way, and his knees knocked together. … 13 Then Daniel was brought in before the king. The king answered and said to Daniel, “You are that Daniel, one of the exiles of Judah, whom the king my father brought from Judah. … 16 But I have heard that you can give interpretations and solve problems. Now if you can read the writing and make known to me its interpretation, you shall be clothed with purple and have a chain of gold around your neck and shall be the third ruler in the kingdom.” 17 Then Daniel answered and said before the king, “Let your gifts be for yourself, and give your rewards to another. Nevertheless, I will read the writing to the king and make known to him the interpretation. 18 O king, the Most High God gave Nebuchadnezzar your father kingship and greatness and glory and majesty. 19 And because of the greatness that he gave him, all peoples, nations, and languages trembled and feared before him. Whom he would, he killed, and whom he would, he kept alive; whom he would, he raised up, and whom he would, he humbled. 20 But when his heart was lifted up and his spirit was hardened so that he dealt proudly, he was brought down from his kingly throne, and his glory was taken from him. 21 He was driven from among the children of mankind, and his mind was made like that of a beast, and his dwelling was with the wild donkeys. He was fed grass like an ox, and his body was wet with the dew of heaven, until he knew that the Most High God rules the kingdom of mankind and sets over it whom he will. 22 And you his son, Belshazzar, have not humbled your heart, though you knew all this, 23 but you have lifted up yourself against the Lord of heaven. And the vessels of his house have been brought in before you, and you and your lords, your wives, and your concubines have drunk wine from them. And you have praised the gods of silver and gold, of bronze, iron, wood, and stone, which do not see or hear or know, but the God in whose hand is your breath, and whose are all your ways, you have not honored. 24 “Then from his presence the hand was sent, and this writing was inscribed. 25 And this is the writing that was inscribed: Mene, Mene, Tekel, and Parsin. 26 This is the interpretation of the matter: Mene, God has numbered the days of your kingdom and brought it to an end; 27 Tekel, you have been weighed in the balances and found wanting; 28 Peres, your kingdom is divided and given to the Medes and Persians.” 29 Then Belshazzar gave the command, and Daniel was clothed with purple, a chain of gold was put around his neck, and a proclamation was made about him, that he should be the third ruler in the kingdom. 30 That very night Belshazzar the Chaldean king was killed. 31 And Darius the Mede received the kingdom, being about sixty-two years old.
Belshazzar was said to be a historical fiction invented by the author of Daniel, because historians knew Nabonidus was the last king of Babylon.  Indeed, there was no record of any Babylonian ruler named Belshazzar.[1]  All that changed in 1881 when a cylinder was found at the Temple of Shamash (temple of the sun) in Sippar.  The cylinder describes how King Nabonidus (556-539 BC) repaired three temples.  It also mentions Belshazzar, and identifies him as the eldest son of Nabonidus: “As for me, Nabonidus, king of Babylon, save me from sinning against your great godhead and grant me as a present a life long of days, and as for Belshazzar, the eldest son—my offspring—instill reverence for your great godhead in his heart and may he not commit any cultic mistake, may he be sated with a life of plenitude.”
Subsequently other documents have been discovered which speak of Belshazzar as well, always calling him “the king’s son”.  Apparently he was co-regent with his father, but never became king (he died before Nabonidus).  That’s why he offered Daniel the 3rd highest position in the kingdom rather than the second (Dan 5:16): That was the highest position left to give.
Significance:
  1. The mention of Belshazzar confirms the accuracy of the Biblical account.

[1]“Daniel chapters 5, 7, and 8 name Belshazzar as a king, but that was probably due to Aramaic convention (e.g., the bilingual inscription on the statue of Haddayishi from Gozan calls him a ‘governor’ in the Akkadian language but ‘king’ in Aramaic.”