The notion of -site is the incarnation of the notion of (∞,1)-site when (∞,1)-categories are incarnated as simplicially enriched categories.
An (∞,1)-site – an (∞,1)-category equipped with the structure of a site on its homotopy category – serves as a domain for ∞-stacks/(∞,1)-category of (∞,1)-sheaves. It may be modeled by a simplicially enriched category.
A simplicially enriched category with the structure of a site is called an -site (def 3.1.1 in ToVeI).