Final answer:
The 'household gods' or Penates mentioned by Hector to Aeneas signify the protection of the family and continuity of the home.
Step-by-step explanation:
The significance of the 'household gods' or Penates that Hector tells Aeneas to take with him as he flees from Troy is deeply rooted in Roman religious practice and cultural identity. These gods were worshipped as protectors of the home and were considered essential for the well-being and continuity of the family.
The Penates, paired with the lares, played a significant role in daily Roman life through rituals and offerings, symbolizing a direct link to the ancestors. In the context of Aeneas' flight, taking the Penates represents the idea of carrying the very essence of Troy, its gods, and the future of his people to establish a new homeland, as depicted in Virgil's Aeneid.