A ship equipped with a cloaking device and on the intercept mission will ignore the regular combat order and attack its intercept target first. During its intercept mission the ship is not cloaked and will not cloak after combat, although the name of this operation may suggest this.
After the ship has successfully intercepted its target (and either has set its primary enemy to the target's race or is being attacked by the target), it will first engage its target and then (if it survives) fight in the regular battle order.
The most common use of this mechanism is to remove ships from enemy fleets, sacrificing your ship to destroy the enemy's ship. For instance, destroying a Cobol or Fuel Refinery in an enemy fleet can cripple an entire offensive, buying you critical time to mount a counterattack, or by forcing the enemy to send fewer ships.