You can equip up to two skulls per mission. When a mission is completed with skulls activated, you will receive a credit bonus. Having two skulls equipped increases the credit bonus. Skulls will handicap you with the following effects.

Hollow
Your Spartan only has a shield for protection.

Pacifist
Your Spartan's armor and shields deplete when you fire a weapon.

Famine
Dropped weapons carry less ammunition.

Black Eye
Your shields only recharge after taking melee attack damage.

Thunderstorm
Adds tougher enemies.

Blind
Cannot see important HUD elements, including ammo for all weapons.