Blowing up the flames means (Changing the flame strength)
There are 3 flame strengths - Low, Medium, High. To change these setting you must select “Blow up the flames” and watch the fire in the forge animation.

When smelting your first materials Iron/Copper
Boiling means turn the flame to the lowest setting.
Hardening means turning up to highest flame. Any dialogue that says “It is not done yet” is Medium.