The root seb- (σέβ-) is connected to danger and flight, and thus the sense of reverence originally described fear of the gods.
[1][2] The word was used in Classical Greece where it meant behaving as tradition dictates in one's social relationships and towards the gods.
One demonstrates eusebeia to the gods by performing the customary acts of respect (festivals, prayers, sacrifices, public devotions).
In ancient Greek religion and myth the concept of eusebeia is anthropomorphized as the daimon of piety, loyalty, duty and filial respect.
For example, "Divine power has granted to us everything pertaining to life and godliness (eusébeia), through the true (full, personal, experiential) knowledge of Him Who called us by His own glory and excellence" (2 Pet 1:3) Peter.