To get high temperature flame, often pure oxygen is used instead of air. This way, the nitrogen content of air - that is just a inert gas here - does not reduce the temperature of flame. Less fuel (most frequently natural gas) is used to heat the object to the required temperature.
Oxygen is used to melt aluminium, steel, glass and other materials with high melting point.  

Oxygen has been used for health care applications for long time. Recently,  small oxygen generators (with other name, "oxygen concentrators") became  available. These small oxygen generators are installed in the home of patients . Portable oxygen generators are available as well.
On the other end, complete hospitals are supplied by one central oxygeen generator, especially in such geographical regions, where there is no reliable oxygen supply due to logistical reasons. 

One of the hardest tasks in intensive fish farming is to maintain the proper oxygen concentration in the water. Only a small amount of oxygen can be dissolved in water (at 15 oC, it is only 10 mg/dm3) and the dense fish population can  consume it fast. Insufficient oxygen supply results in high fish mortality.
Using pure oxygen, maintaining the proper oxygen supply is much easier, than with air.

Oxygen produced by oxygen generators frequently used, as a raw material for chemical reactions, not only in simple burning processes. For example, pure oxygen is a much better raw material to produce ozone, than air.
Ozone is a highly effective desinfectant, widely used in water supply system, in food industry and other applications.

Acetylene-oxygen flame is the conventional way of welding. Costs of welding  can be significantly reduced using oxygen generators.
Similarly, generated oxygen can be widely used in flame cutting applications.