the ideal that every US citizen should have an equal opportunity to achieve success and prosperity through hard work, determination, and initiative. (Google)

the widespread aspiration of Americans to live better than their parents did

(Wolfram Alpha)

a happy way of living that is thought of by many Americans as something that can be achieved by anyone in the U.S. especially by working hard and becoming successful <With good jobs, a nice house, two children, and plenty of money, they believed they were living the American dream.>

(Merriam-Webster)