One could define impudently as "to be excessively bold or unbridled in one's behavior." It implies a lack of respect for one's surroundings or others and can often reflect disdain or disdainfulness. This seems to be particularly the case when the impudent person is transgressing social norms and customs. In other words, they're acting without thinking and without regard for others.

Of course, we're all familiar with people who are impudent by nature. They're often unruly and unafraid to say what's on their mind. They do things their own way, regardless of what others might think.