What does Daniel 5:31 mean?

This verse records that fact that Darius the Mede took over the kingdom of Babylon. It's possible Daniel skipped over some political developments between the death of Belshazzar and the rule of Darius. Historians struggle with this passage and how best to harmonize it with archaeology. It's possible Darius and Cyrus (Daniel 6:28) are different names for the same person. It's also possible that one was "appointed" to power over the city of Babylon while the other ruled the entire kingdom. The details given in Scripture are limited, leaving room for options which are subject to debate.

Darius, the son of Hystaspes, was apparently the rightful heir to the throne of Persia, having descended along with Cyrus from the royal line of Persia. He abolished local kingdoms and principalities; he divided the empire into satrapies, with each satrap overseen by a Persian with supreme authority over civil affairs. The Persian official also commanded a division of the army. Judges were appointed with assigned circuits, royal roads stretched everywhere, and Susa and Persepolis were Darius's capital cities. With the transfer of power from Belshazzar to Darius the truth is apparent that the Lord puts down one king and raises up another (Psalm 75:7).