Nonchalance is a casual lack of concern, a relaxed state without anxiety or enthusiasm. Like how you'd act if the girl you've had a secret crush on since grade school asks you to the prom. (Or maybe not.)
It's hard to achieve nonchalance. If you're like most people, there's always going to be something that will rattle you. And you can forget about behaving with chalance, because chalance isn't a word. Sometimes you hear people say that so-and-so acted with "studied nonchalance," which means to sort of fake it. Oddly, the word's origins go back to the Latin calere, which is the same word as the root of calorie. A calorie is a unit of energy, and to act with nonchalance is to refrain from showing too much energy or excitement, so actually, it makes sense.