The meaning of Piety in the Bible
(From International Standard Bible Encyclopedia)

pi'-e-ti: Only in I Timothy 5:4 : "Let them learn first to show piety toward their own family," where "let them show piety" represents a single Greek verb (eusebeo), in its only other occurrence (Acts 17:23) being rendered "worship." In Elizabethan English "piety" (like the Latin pietas) could be used of devotion to one's parents (as still in the phrase "filial piety"), as well as of devotion to God. Hence, there is no explicit statement here that filial devotion is one form of divine worship.

See more on the meaning of Piety in the Bible:
Piety {Easton's Bible Dictionary}

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