A boiler was a contraption used to boil water. Fuel, commonly coal, was placed under a water container, which caused the water to boil. The water could then be directed elsewhere, such as to power a locomotive.
In 2370, the conductor of the Orient Express showed Worf where the boiler and the coal were. (TNG: "Emergence")
In a deleted scene from ENT: "Fallen Hero", Trip Tucker described the pace of Enterprise NX-01's warp drive operations, saying, "We're really stoking the boilers down here."