Intimidation operations are used to permanently remove the abilites of enemy planets.
The battle is fought on a unique battlefield on the planet with the Consortium Hero and some reserve units, and sometimes the Defiler. There are special objectives to each mission, so they ae unique to each other. The units in battle apart from the Hero are not counted against you should they be destroyed, but it is advisable to keep them alive to capture turrets, which are useful should you have to refight the battle there.
Intimidation removes the ability permanently from that planet. For example, is an enemy planet that normally speed up production of Imperial Star Destroyers is corrupted with intimidation, no matter what, the enemy will not get that bonus back from that planet. Intimidation also unlocks racketeering operations.