Pietas, usually translated as piety, is the duty of one who honors what binds him to others: the gods, the father, the son, the homeland. In the Aeneid it is the trait that defines Aeneas, to the point that the poem asks the Muse to explain why a goddess pursues a man "distinguished by piety."
The poem shows piety in deeds. On the last night of Troy, Aeneas carries his father on his shoulders through the flames, leads his son by the hand, and brings the Penates, the household gods, which Anchises carries because the son, stained with blood, may not touch them. Later, he grounds his request to go down to the world of the dead precisely in that gesture: he wants to see his father's face and reminds him what he did for him.
Piety is also obedience. Aeneas accepts orders from oracles, from dreams, from gods, and sacrifices a white sow to Juno herself, who pursues him, because the god of the Tiber River advised him to overcome her anger with vows. The narrator calls him pious precisely when he yields to the one who pursues him. In Carthage, this same virtue sets him against Dido: he says that Italy calls him and that he does not go of his own will.
The poem does not leave the virtue on one side only. In Book 10, Lausus throws himself against Aeneas to save his wounded father, Mezentius, and Aeneas warns him: "your filial love deceives you, you who are unwary." After killing him, he sees in the young man's face the image of love for one's own father, and returns his arms and body. Pallas also dies out of loyalty to his father. Piety, in the poem, honors those who have it and protects neither side.