The importance of Mount Olympus to the Greeks was that it was the home of the gods. It was where they lived and the center of the gods' power. If they didn't have it, then Olympus would fall and the age of the gods would be gone. The Greeks believed that the gods were the ones who helped them, so if Olympus was destroyed, then they would be hopeless.
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In Greek mythology, mount Olympus was the dwelling place of most the gods and where Zeus, "Father of Gods and men" had his throne. Zeus ruled the Olympians of Mount Olympus as a father ruled the family.