audacity
Bold courage to do something risky or surprising.
Audacity is bold, daring behavior that surprises people because it seems risky or even a bit outrageous. When someone has audacity, they do something that takes real nerve, whether that's standing up to someone powerful, trying something incredibly difficult, or taking an action most people would never dare to attempt.
The word can carry different feelings depending on the situation. Sometimes audacity is admirable: it took audacity for the Wright brothers to believe they could build a flying machine when experts said it was impossible. It takes audacity to raise your hand and disagree with an idea everyone else accepts, or to enter a competition against much older or more experienced competitors.
Other times, audacity means someone has crossed a line into rudeness or disrespect. If a student interrupts the principal to demand special treatment, that's audacity of the wrong kind. If someone cuts in front of a long line of people waiting, you might think, “They have the audacity to act like their time matters more than everyone else's!”
The phrase “the audacity!” expresses shock at someone's nerve, usually when they've done something inappropriately bold. Whether audacity is courageous or just plain rude depends on the situation and whether the bold action serves a worthy purpose.