Simply put, materialism — as opposed to idealism — is the idea that everything we do and experience as a society (our history, culture, politics, etc) is shaped by the material reality around us, rather than ideas.

"Material analysis" in this case therefore means analysing politics and history through this lens. And it's a fundamental component of socialism/marxism.

Simple diagram of how our material reality shapes our society

• Socialism For Beginners (Video)

• Dialectical and Historical Materialism
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Yogthos is insulting liberals because liberalism is an idealist ideology that always eventually gives way to fascism when a capitalist state is (inevitably) in decay.