If we’re expected to be Hashem’s chosen people, it means, “kedoshim tiheyu” we're expected therefore to live a life of kedusha (holiness), which means a life of dedication to the ideals that Hashem expects.
For that, Shabbas is a reminder. “Es shabsosi tishmoru -- Keep my Shabbas.” Why? “Ki os hi,” because it’s a sign between Me and you. What's the purpose of this "sign"? "Lada’as ki ani Hashem m'kadishchem — That you should know I am making you kadosh (holy). — Preface to Shabbas 7 (#532)