Details like the one you ask about here are always interesting things to consider when reading a novel. The primary conflict in To Kill a Mockingbird by Harper Lee centers around racial tensions. The story is set in the South in the 1930s, and of course we know history well enough to know that the divide between blacks and whites in the South was more like the Grand Canyon than a simple little ditch.
Times were different. Women did not serve on juries and were considered too "delicate" to hear unpleasant things in any setting. Black people were generally considered to be inferior in every way, and the Ku Klux Klan was still a visible and active presence.
In this story, Tom Robinson is a black man who has been accused of rape by a white woman, and of course the assumption by most is that he is guilty. Even worse, at least to this group of people, is that Atticus Finch has been appointed as Tom's lawyer and is actually preparing to mount a credible defense of him in court.
Until the night before the trial, Tom was kept in a jail cell outside of Maycomb, so when he is finally transferred to Maycomb Sheriff Heck Tate is concerned about some possible trouble. So is Atticus, though he says very little about it.
After telling his children good night, Atticus takes a light and goes to keep a quiet vigil outside Tom's jail cell. He takes the light because there is no light at the jail. The children get close and see Atticus's light. Scout tells us this:
As we walked up the sidewalk, we saw a solitary light burning in the distance. “That’s funny,” said Jem, “jail doesn’t have an outside light.”
Obviously the children knew there was no light there, so this is simply something everyone knew about the jail. No lights were removed just because of Tom's transfer; this is just the way the jail was built.
Your question is why that is the case, and there is no indication of a reason in the text. We know the town has streetlights, because Scout mentions them as she describes their walk to Atticus's office. So we know that the jail could have been better lit if the town had chosen that. Both the courthouse and the jail are dark by design. While the courthouse is a noisy place during the day (which is why Atticus moved to quieter offices), obviously there is little action there at night.
The same is probably true of the jail. It is a small building rather tucked in between two other buildings, and it certainly does not look like a typical jail.
Starkly out of place in a town of square-faced stores and steep-roofed houses, the Maycomb jail was a miniature Gothic joke one cell wide and two cells high, complete with tiny battlements and flying buttresses. Its fantasy was heightened by its red brick facade and the thick steel bars at its ecclesiastical windows. It stood on no lonely hill, but was wedged between Tyndal’s Hardware Store and The Maycomb Tribune office. The jail was Maycomb’s only conversation piece: its detractors said it looked like a Victorian privy; its supporters said it gave the town a good solid respectable look, and no stranger would ever suspect that it was full of niggers.
All of this to say that there does not seem to be any obvious reason why the jail is dark except that Maycomb probably does not have many criminals (thus the two tiny cells)--and those they have are "only" filled with black people. For most people in town, those prisoners do not need to have any light. Metaphorically and literally, they want to keep blacks in the dark.