The localization of a simplicial model category accordingly models the localization of the corresponding (infinity,1)-category, i.e. the passage to the a reflective (infinity,1)-subcategory).
A famous example of localizations of simplicial model categories appears in the study of model structures on simplicial presheaves, where it yields a presentation of (infinity,1)-sheafification completely analogous to how ordinary localization described ordinary sheafification:
the Bousfield localization of these global model structures at morphisms which are local (stalkwise) weak equivalences yields the local projective/injective model structure on simplicial presheaves on , which then presents the (infinity,1)-category of (infinity,1)-sheaves on .
chapter 9.4 in
section A.3.7 of