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According to the definitions:

The correlation matrix reports the correlation of each variable with each dimension.

Contribution refers to the contribution of each category of each variable to the dimension.

I have two questions regarding the interpretation.

How to interpret these correlations and, how is it different from the usual correlation?

What does it mean that each category contributes to this dimension or that dimension?

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What does it mean that each category contributes to this dimension or that dimension?

You might find answers to your questions on this page : http://www.sthda.com/english/articles/31-principal-component-methods-in-r-practical-guide/114-mca-multiple-correspondence-analysis-in-r-essentials/

See for example:

The variable categories with the larger value, contribute the most to the definition of the dimensions. Variable categories that contribute the most to Dim.1 and Dim.2 are the most important in explaining the variability in the data set.

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