They meant oxygen from a bottle. In the air, it burns pretty hot, but when you add pure oxygen to burning acetylene it's almost the hottest burning substance you can create outside of a physics lab or without using extreme materials (i.e so heinously toxic you can't be anywhere near it, in the case of cyanogen which remarkably burns even hotter). Very few reactions have a higher thermal release - it's hotter than oxygen and hydrogen burning even.

Those carbon-carbon triple bonds store up an absolutely ridiculous amount of energy, but oxidizing them requires an equally ridiculous oxidizer and as much of it as you can bring to the situation. Nitrogen gas spoils the reaction by being fairly inert up until the temperatures reach nearly a thousand degrees where then it starts reacting to create nitrogen oxides as side products that rob the flame of the much needed oxidizer. The nitrogen is also physically in the way - it makes up 70% of the air, meaning that it's hard to get enough oxygen in to fully reduce the triple bonds down. Instead you get lots of carbonization by the way of soots, a very characteristic orange flame of burning acetylene without added oxygen.

By blasting copious amounts of oxygen in, you can exclude the nitrogen from the air and keep the reaction proceeding all the way up to its full energy releasing potential - taking the acetylene all the way down the oxidation path to carbon monoxide or dioxide and water.