In his sefer “Eish Kodesh”, Holy Fire, which was written in the Warsaw ghetto, the Piasetzner Rebbe [Pieseczny] offers a beautifully simple explanation of ‘Shabbat Hagadol’. The Rebbe explained:
When I accept upon myself the yoke of Hashem’s kingdom no matter how difficult a situation I may find myself in, then I am making Hashem’s name great!
On this holy Shabbos, we proclaim our faith in Hashem, our ultimate redemption and the coming of Mashiach. Even today, despite everything we have lived through and are living through presently, we are making God’s name great by observing our Holy days and mitzvot.