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啟盛世開太平 means “To bring flourishing peace and security to the world (our current era).”
It's a wish that a new door leading to peace and prosperity could be opened to mankind.
Character and word breakdown:
啟 to open; to start; to initiate; to enlighten or awaken.
盛世 a flourishing period; period of prosperity; a golden age.
開 to open; to start; to turn on.
太平 peace and security; peace and tranquility; peace; tranquility.
I don't like to do breakdowns like this, as the words altogether create their unique meaning (encompassed in the main title above).