The lines "Steam was our handmaid and our servant flame" was said by John Masefield in regard to a ship. Steam is considered as an important factor that keeps the engine of the ship moving. Though it lies inside and cannot be seen outwardly on the exterior of the ship, it is what makes the ship working and moving.
Similarly, the speaker compares the steam to a handmaid who also works and maintains a house from inside. It is like a flame/feul that burns inside just like a home aid who works inside the house.
