It means: To prepare a bath, someone had to boil water in a pot on the stove (so that there would be hot water to put into the bath tub; no hot running water like there is now). To have a fire in the stove (or coal fire heater) someone had to go to cellar (basement, under the house or apartment) and carry a bucket of coal upstairs. Coal was stored under the house.

The intent of that sentence is to emphasis the labour that would have been involved in doing something (in the past) that we consider very easy today. That sentence, is a really an abbreviated form of a sentence (or two) that might go: [Back then, preparing a] bath would involve heating numerous kettles and pans of water, each boiled on the top of the stove. This was a time-consuming and laborious process that required coal to be carried up from a cellar in order to build a suitable fire.