What is the purpose of the plush-like seat covers in an airliner cockpit?
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And this forum topic.

They help prevent wear and tear on the seat fabric underneath and are fairly easy to replace. In a lot of GA planes they are installed to hide old tired seats underneath. But mostly they are just really really comfortable. They breathe in warm weather and help insulate in cold. All around a good fabric choice for the application (see related question for notes on fire prevention).