What's oxidative stability?

Not at all stupid. It's just a very uncommon phrase.

Oxidation stability is a chemical reaction that occurs with a combination of the lubricating oil and oxygen. The rate of oxidation is accelerated by high temperatures, water, acids and catalysts such as copper. The rate of oxidation increases with time. The service life of a lubricant is also reduced with increases in temperature. Oxidation will lead to an increase in the oil's viscosity and deposits of varnish and sludge.

Sounds vague doesn't it?

Source: http://www.machinerylubrication.com/Read/28966/oil-oxidation-stability

Another source states:

Oxidative stability is a measure of an oil or fat's resistance to oxidation. Because the process takes place through a chain reaction, the oxidation reaction has a period when it is relatively slow, before it suddenly speeds up. The time for this to happen is called the "induction time", and it is repeatable under identical conditions (temperature, air flow, etc.).

Source: https://en.wikipedia.org/wiki/Rancidification

Hope this helps you in some way

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Hmm, sounds about right but it doesn't have to be oils/fat though.
If organic compounds or especially polymers are exposed to oxygen, light and heat for longer time, an aging process takes place. On the one hand this means a slow oxidation of some components on the other hand some molecules are not long time stable and decompose after an undefined time period. Oxidative stability just means that oxidation/reaction of organix compunds take place at a slow pace before reaction is accelerated.
Source: https://www.linseis.com/en/media-center/measurement-applications/measurement-of-thermaloxidative-stability/