First, it's important to ask known by whom. Americans know American universities better than they know foreign ones, but the number of American universities known by people outside of America is considerably smaller than those known by Americans.

But in general: during the 20th century the US took the German "research university" model and applied it on a massive scale, with huge amounts of funding (much government, originally, but also industrial) and used it to power a "Golden Age" of scientific and technological advancement that outstripped much of what had been done before (or since; by the end of the Cold War that level of "progress" seems to have slowed). The US also capitalized on the ruin of Europe in World War II, cherry picking many of its top researchers and scholars and giving them new opportunities that their original nations could not afford to keep up with. This means that the proportion of people who received Nobel Prizes, patents, and other high accolades from universities and research laboratories in the US has been very large — even if the original people were not Americans by birth.

So what you're seeing is the tail-end of a "scientific boom" that took place from the 1940s through the 1990s. These universities built up impressive endowments and reputations, which allowed many to compete on international levels.

Whether that translates into good teaching is another question entirely, and whether that translates into continued research progress is doubtful for a number of reasons, but this gets into present-day issues and not historical ones. But it is important for understanding these present-day issues to understand that none of these historical movements were fated or magical — they are about historical conditions that were encouraged and taken advantage of.

There is much written on the rise of the US research university in the 20th century. Daniel Kevles' The Physicists provides a good focus on physics in particular, but serves as a broader story as well. The work of MIT's David Kaiser on the postwar physics "boom" is also of note. On the question of decline, John Horgan's The End of Science makes for a provocative argument.