The ability to basically say whatever you want without repercussions, such as insult the king. A jester would have legal protection and permission to make such jeers, as his purpose was simply to entertain and was often not taken seriously, but despite this, often was one of the more important members of the King's Court, and was given high status.
"He just insulted the king! He should be punished"
"Its fine, he's a jester. He has Jester's Privilege"