"Mitzrayim" (Egypt) means constriction, limitation. The spiritual Egyptian exile is the animal soul's restricting and concealing the G-dly soul so severely that the G-dly soul is compressed to the degree that it is diminished and obscured. "Exodus from Egypt" is the removal of the constriction and bounds; i.e. the intellect in the brain illuminates the heart, bringing about fine character traits translated into actual practice.
Rabbi Yosef Yitzchak of Lubavitch (as quoted in Hayom Yom, Shevat 4)