I am now reading the book Higher Topos Theory. In A.3.1.5, it gives the definition of a $\mathbf{S}$-enriched model category, where $\mathbf{S}$ is a monoidal model category. But in the book model structures are introduced only on $\mathsf{Set}$-enriched categories.

So, what does a model structure on a $\mathbf{S}$-enriched category mean?

Is it supposed to be that $\mathbf{S}$ obtains a forgetful functor to $\mathsf{Set}$, and the model structure is defined on the category with respect to the $\mathsf{Set}$ enrichment, or is it something else?