Critical Hits are a recurring feature of RPGs, in which attacks have a chance to deal increased damage. This was introduced to the franchise in Disgaea 2: Cursed Memories.
Characters have a stat called 
Critical Rate (not visible in Disgaea 2), determining their chance to perform a Critical Hit. Critical rate is by default a low amount(usually in the single-digit range) and up to Disgaea 5 it's increased by equipping most weapons. Attacks against Sleeping units always result in a Critical Hit.
Disgaea 2 to 4[]
Critical Hits add 50% to the attack's Base Power. Equipment with a 
Professional increases the Critical rate by +1% per Specialist level.
Disgaea 5[]
Critical Hits increase damage dealt by 50%(multiplicative bonus). Equipment with a Professional adds 1% to the base damage bonus per Specialist level(max +100%). Equipping an Axe adds 15% to the base damage bonus, but only for physical attacks. Evilities that increase Criitical damage each apply a separate damage multiplier.
Disgaea 6[]
Critical Hits increase damage dealt by 100%(multiplicative bonus). Equipment with a Professional adds 0.1% to the base damage bonus per Specialist level(max +100%). Evilities that increase Critical damage are added to the base damage bonus.
Disgaea 7[]
Critical Hits increase damage dealt by 50%(multiplicative bonus). Evilities and Properties that increase Critical damage are added together(capped at +100%) and applied as a separate multiplicative bonus. The "Critical" line of Properties increases Critical rate and is usually found in Fists and Glasses, while the "Critical D" line increases Critical damage and is usually found in Spears.