"General Defense" is a name contrived to compliment the more commonly used abbreviation (GEN), and is not the terminology as designated by the YU manual.
General Defense aka Leadership is a recurring stat in Yggdra Union and its spin-off titles, serving as a protective stat. GEN helps to protect against charge attacks and card skills in combat sequences.
With skills, GEN helps to either reduce the damage depending on GEN/TEC difference, or completely nullify it if the GEN of the unit is higher than the user's TEC. Low GEN can, consequently, cause a unit to suffer heavy blows from technical characters like Russell.
Lastly, this stat affects the ability difference modifier when a clash is lost and Morale damage is calculated. Units with high GEN can have their ability difference modifier reduced to the negatives if they lose in a clash. The difference between GEN and ATK affects ability difference. Ex: If a unit with an ATK value of 5 defeats an opponent with a GEN value of 2, the ability difference will be +30%. If GEN and ATK are equal between the two combatants, then the ability difference is 0%.