Mea maxima culpa comes from Latin and means “through my most grievous fault.” It is a stronger version of mea culpa, which means “(through) my fault.”
Mea maxima culpa comes from a Roman Catholic prayer of confession and is the third, final, and strongest expression of guilt in the lines “mea culpa, mea culpa, mea maxima culpa.” Mea maxima culpa is not usually used outside of a religious context, whereas you will find mea culpa more widely used.