The success that Americans are said to worship is success of a specific sort: accomplished not through hard work, primarily, but through the ingenious angle, the big break. Sit down at a lunch counter, stand back up a star. Invest in a new issue and watch it soar. Split a single atom, win a war.

This quote is saying that in America, success is often seen to be achieved through luck rather than through hard work. The example provided is that someone can just sit down at a lunch counter and suddenly be seen as a star. Another example is if someone makes a lucky investment and it takes off. Lastly, it implies that if someone makes a huge discovery, like splitting an atom, it could potentially lead to winning a war.