Flame cutting is a combustion process. It is not the heating flame itself that does the actual cutting but an oxygen jet, which burns the material during the heat formation and transports the combustion products (slag) away from the cut.
When cutting, oxygen purity is of great importance for cutting speed. The purer the gas, the higher the cutting speed and the better the productivity and cut quality.
Flame cutting is easy to cut very thick plates either from steel, stainless steel or aluminum, and it is more economical.
Flame cutting is normally used when the material is quite thick or heavy and the surface quality is that important.