"In answer to his words, Zeus the Thunderer urged two eagles into flight from the mountain-top"
The ancient Greeks believed that portents and signs could be read in the natural world, such as in the flight of birds or the entrails of animals. When something significant was seen to happen, such as the two eagles fighting in this passage, they saw it as an omen
from the gods, something that was intended to warn or prepare them. Zeus, in particular, was associated with these signs.