What are MDS matrices and how are their applications to data computed?

Published: 14/11/2017
What are MDS matrices and how are their applications to data computed?
Source: CRYPTO.STACKEXCHANGE.COM

I get that MDS matrices are some fancy schmancy things that increase diffusion and resistance to certain types of cryptanalysis when they are made correctly, but I do not know what they are or how they are actually applied to data? Are they just arrays of bits or are they more complicated like the "polynomials" used in finite field arithmetic? Are they applied by using matrix multiplication? Or

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