Improv is the short, everyday word for making a performance up as you go: acting, singing, or playing music without a script you learned first. Comedy clubs and drama classes use it all the time; jazz players do a kind of improv too. People also say 'to improv' in casual speech, meaning to invent the next line on the spot. The longer, more formal cousins are improvise and improvisation. Though actually, good improv is not empty luck. Players train hard, and they follow simple rules, like saying yes to a partner's idea and adding to it. The word is informal. You would not put it in a very serious essay unless you were writing about theatre.