What does it mean that the Duke of Zhou lit a fire and the people were not allowed to light a lamp?

Only state officials are allowed to set fires, but people are not allowed to light lamps, which means that officials are allowed to set fires and people are not allowed to light lamps. It means that powerful people can do things themselves, but people are restricted from even legitimate activities.

From Lu You's Notes on the Old Learning Temple in Song Dynasty, Volume 5:

Tian Dengzuo County, who kept his name secret, would be angry if he touched it, and many officials and soldiers were condemned. Therefore, for the state, it is said that the lamp is fire. On the Yuan Dynasty, people were allowed to enter the state for sightseeing. The official then revealed the book list in the city and said, "The state set fire to it for three days according to the law." Therefore, the saying goes: "Only state officials are allowed to set fires, and people are not allowed to light lamps." Benben.

Translation:

When Tian Deng was a state official, he made it a rule that his name should be avoided. Anyone who made a mistake in his name became angry, and most of his officials were punished for it. So people have to call "lamp" fire. On the fifteenth day of the first month, lanterns were set up to allow people to go into the city to watch, and officials wrote notices and published them in the market: "According to the usual practice, the state set fire for three days." So he said, "Only state officials are allowed to set fires, and people are not allowed to light lamps." That's where it comes from.

Extended information:

When Tian Deng became a satrap, he was afraid that others would say or write his name, so the people in the whole state had to read or write the word "light".

On the Lantern Festival, the state will put on lights for three days for ordinary people to watch. Because officials were afraid of reading and writing the word "light", they violated the taboo of Tian Deng's satrap, so they wrote a notice and posted it at the market, saying, "The state set fire for three days according to the usual practice."

This idiom story comes from Notes of the Old Learning Temple. Notes on the Old Learning Temple, written by Lu You, a famous poet in the Southern Song Dynasty, mostly records anecdotes, examines poems and occasionally adopts folklore.

Tai Shou Tian Deng, fish the people, is overbearing, so that people are not allowed to say "Deng", write "Deng" and words with the same sound as "Deng", otherwise it is a big disrespect to him, ranging from being beaten to being executed. Therefore, on the third day of the last Yuan Festival, the "An Min Notice" had to be rewritten as "Set fire for three days", which caused an ironic joke.

The idiom "Only state officials are allowed to set fires and people are not allowed to light lamps" is summarized from this story. Nowadays, people use it as a metaphor for reactionary rulers who are autocratic and savage and can do bad things at will, but the legitimate behavior of the people is subject to various restrictions.