Well "strength" of any acid is based on relative terms. There really is no cutoff for "strong" acids. So with that in mind, the strength of any acid is determined by the stability of its conjugate base. The reason is because for an acid to behave as an acid, it must donate its proton thereby turning it into its conjugate base. Therefore, the more "willing" it is to give up its proton, the stronger the acid is relative to an acid with a not-as-stable conjugate base. The acid with a not-as-stable conjugate pay pays a bigger fee energetically to give up its proton; therefore, the acid with a more stable conjugate base is more willing to give up its proton, ultimately making it a stronger acid relative to the other one.