Its hard to encapsulate what makes America great in one post but Deorum did about as good a job as can be done here.
I'll say one thing I find fascinating about the USA is how deliberately it was created. As Ernest Gellner, a scholar of nationalism, once said: "America was born modern; it did not have to achieve modernity, nor did it have modernity thrust upon it."
That's not the case with most societies which had to enter modernity with lots of premodern baggage or had it thrust upon them via colonialism. Look at the English constitutional system, its current form was hammered out by many generations, sometimes via gradual reforms and sometimes via more revolutionary moments. But there was always a connection to the past. Or look at India which had modernity thrust upon it by the British and had to adapt to that reality.
With the USA we had a bunch of elites get together and basically from scratch they devised our system and the fact that its the oldest extant constitution to this day, despite how young the US is compared to other nations, is a testament to how durable and adaptable the American system is. Very unique in world history.