Originally, piety refers to one’s feeling of spirituality and humanity that lead to acknowledging and accomplishing one’s duty to a god, or to one’s parents (see family) or homeland (see patriotism)...
Nowadays we use this word in its religious meaning : piety refers to one’s deep attachment and respect to a god and the religious practices and duty.
There is also family piety that refers to one’s love and respect for one’s parents.
Piety is a personal practice, even though there’s people who tend to impose their vision on how to express those feelings. Everyone has their own way of showing their love and respect to their god or parents. Some people like to show of their piety, other prefer to be discreet.