Piety is devotion to God or to religious practices. Nuns who pray all day long are famous for their piety. If you have filial piety it means you're devoted to your parents.
Piety is sometimes used in a disapproving way to mean that the person is only pretending to be devoted or good. It was borrowed from the French word pieté, meaning "piety or pity," ultimately from the Latin pius, "devoted, kind." This Latin adjective is also the source of our English adjective pious.