At a genetics course, the question asked by the tutor was: “Suppose we perform a combined genome/epigenome-wide association study where we measure the genotype and methylation of a cohort of disease cases and healthy controls. Consider the genotype at a particular SNP X, the methylation at a particular CpG site M, and the disease status Y. Under what conditions can we say that methylation causes disease rather than being a consequence of disease?” The official answer from the tutor was: “We say M mediates the link between X and Y if X is associated with Y, M is associated with Y, but X is not associated with Y conditioned on M. In this case, genotype causes a change in methylation, which in turn causes a change in disease status”

Here is my question: Can you explain the above answer from the tutor in a more simple way and with less complex words? What does the tutor want to say by “X is not associated with Y conditioned on M” ? What does “conditioned on M” mean?