On one hand, lights. For a long while, there were none: Shakespeare's Globe theater had an open roof, to let in natural light, and a show would run during the day. In the 17th c. chandeliers near the front of the house were used for stage lighting, which resulted in hot wax or molten tallow often dropping onto the clothes of the audience . In the early 19th. c. gas began to be used for street lighting, and a very bright ( cough) man named Goldsworthy Gurney discovered that calcium carbonate, AKA lime, would give off a very bright light if heating in a gas lame, and in 1837 "limelights" began to be used. So, basically, the stage lights were very hot gas flames. These flaming lights would be all around the stage, and would also be moved around like modern spotlights, as needed.

On the other hand, fuel. Every show would have different scenes, and every scene would typically have a different background dropped in behind it. Those painted backgrounds were ( and are) called flats, because they were typically light cloth stretched on light wood frames, and large numbers of them could be suspended by great numbers of ropes from above, or wheeled in quickly from the wings. There would also be lots of props and stage furniture, costumes, and cloth curtains. All of this would be setting on a wooden stage, and constantly moved around - and often hurriedly- in the vicinity of the flaming lights during the course of the show. And it all caught fire very easily.

Last, but not least, exits. Today, theaters tend to have lots of exits, clearly marked. Not in the 19th c.. The theater wanted to limit the people attending to the ones who'd paid. Because there were few ways in, there were few ways out, especially from cheap seats in the upper balconies. Also, though the stage might be well-lit, the house might be quite dim. When a fire started, it would be hard for people to quickly find their way to the nearest door and quickly get through it.

Disastrous theater fires killed hundreds, until in the later 1800's a flame-proof curtain could be dropped, so that a fire started on stage could be contained until everyone had managed to leave the theater. After circa 1897 there could be less limelighting, and more and more electrical lighting: first with carbon-arc lights, then with lightbulbs. With lightbulbs, the house could also be more easily lit, so people could leave quickly, And theaters began to be built with more exits.

Eyre Massey Shaw: Fires in Theatres