Okay, imagine you are playing teacher's pet and you tell your mom, "Mom, I promise to do all my homework tonight." That's a performative utterance!
A performative utterance is when saying something actually causes it to happen. For example, when a judge says "I now pronounce you husband and wife" at a wedding, that's a performative utterance because it makes the marriage happen. Or when you say "I apologize" to someone, the act of saying sorry is what makes the apology real.
So when you say "I promise" or "I declare" or "I resign," you're not just talking - you're taking action with your words!