A firebox is where the fuel that powers most steam locomotives is burned.
It is mostly coal or oil that is burned in the firebox to boil water (which serves as a power source) in the boiler, but wood is occasionally used in older and industrial locomotives.
Fireless steam locomotives don't have a firebox because of it being unnecessary to heat the already pressurized steam. Hence external, stationary steam engines are used to create the pressurized steam for the fireless type.
Shovels are mostly used to stoke fireboxes, that is to have a "fireman" (engineer) shovel wood and coal into a firebox through fire doors that open onto the footplate. These doors are used to seal the firebox; which can also be open to access the actual firebox entrance or hole. Some larger, often American, steam locomotives have mechanical (automated) stokers to move the fuel from the tender into the firebox. All oil fueled steam locomotives have mechanical means to fuel the firebox, such as pumps or mechanical stokers built to move liquid.
A firebox is usually ignited by a fire-lit rag, or other similar materials.