Moderated mediation is a statistical method that checks the relationship between an independent variable, a mediator variable, a dependent variable and a moderator variable.
It is used to determine whether the effect of the independent variable on the dependent is mediated by the mediator variable.
It's important is that it help researchers understand the complex relationships between variables in a model and identify the conditions under which the mediation effect is stronger or weaker.
To add to Chuck A Arize answer: most often the goal of mediation analyses is to determine the presence and magnitude of an indirect effect. A moderated mediation tests, if this indirect path is affected by a moderator, so that the size and/or sign of the indirect effect is dependent on the value(s) of the moderator. It is possible to model that the moderator affects the pre-mediator path, the post-moderator path, the direct path or any combination thereof, depending on your theory. I suggest to read Hayes (2022) to get a grasp.
Hayes, A. F. (2022). Introduction to mediation, moderation, and conditional process analysis: A regression-based approach (3rd ed.). Guilford Press.
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