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Recently, the CRYSTALS lattice-based cryptographic suite has been published, which is based on "module lattices". What is Module-LWE? How is it different from Ring-LWE?

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To quote [AD17]: "One way to informally view the MLWE problem is to take the RLWE problem and replace the single ring elements with module elements over the same ring. Using this intuition, RLWE can be seen as MLWE with module rank 1." For more intuition c.f. their introductory section, and for formal definitions c.f. §2.3 in that paper.

[AD17]: Albrecht and Deo, Large Modulus Ring-LWE $\geq$ Module-LWE.

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