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.

My original comment is meant to refer to the concept of Materialism, which contains the concepts of Marxist Dialectical and Historical Materialism. Materialism is a "reality-focused" branch of philosophy and analysis, contrasted with Idealism, which is idea-focused.

The connection to liberalism and fascism is because Liberalism is Idealist as opposed to Materialist. The Liberal answer to "where does fascism come from?" Would be "demagogues like Trump rising to power, racism, xenophobia, etc," yet when you ask why those ideas are present or not present, the Liberal cannot answer genuinely.

For Marxists, fascism is a consequence of Capitalism's decline, resulting in the Petty Bourgeois elements of society, ie the "Middle Class," sliding into worse conditions and allying with the Bourgeoisie against the Proletariat. In the Weimar Republic, Capitalism was declining and genuine Communism was gaining steam, with the KPD at the forefront and the SPD representing the moderate Socialists, so fascism gained power as a reaction. Communism and Socialism gained appeal among the Lower Classes while fascism gained power among the Liberals, ie the Middle and Upper Classes.

The other works listed by other commenters are great, but my personal favorite work on the subject is Elementary Principles of Philosophy.

Necessary reading.
You could start here though.
The latter is probably a little easier to digest/dip your toes in. The former is the answer to your question.

Material analysis is an analysis using the method of dialectical materialism and historical materialism.

To put in in a grossly oversimplified way, one of the most important concepts of dialectical materialism is that ideas aren't independent from society. Peoples don't pull ideas out of some Platonist void, their ideas are shaped by and consequences of the society and material conditions they live in.

For example, writing didn't appear just because some guy one day said "what if we drew funny shapes in clay and pretended the shapes are words?". When the first human societies started accumulating reserves of food, lumber, domestic animals and materials and to exchange these with other groups of humans, keeping track of everything was becoming a problem. The first writing systems were invented as a way to solve that problem, they figured out that by associating each resource with a symbol they could easily keep track of what they had and how much of it they had.

The same logic apply to fascism. Fascism didn't appear because some guy woke up one day and decided to be an asshole for no,reason. As the contradictions of capitalism worsened (contradictions are also a concept from dialectical materialism btw), peoples were becoming radicalized against capitalism and the bourgeoisie which created the threat of a potential revolution overthrowing capitalism, in order to protect capitalism from that threat, the petty bourgeoisie tried to hide the class struggle between the bourgeoisie and the proletariat by fabricating a fake struggle against a group of the proletariat (typically a "race") that they could point to to divert attention from the class struggle.

This is what is meant in this context. Since liberalism is the main ideology of capitalism, when the contradictions of capitalism inevitably makes everything break down, liberals will either be radicalized to the left and stop being liberals, or defend capitalism to the end by slipping more and more to the right until they become indistinguishable from fascists.