The influence and traditions of fraternities and sororities on American college life are huge. Their relevance today, not so much.
Fraternities are almost as old as the university system. Keep in mind that there wasn’t really such a thing as teenage/early adult culture until the 1920s, and fraternities and sororities were very influential in defining the college experience. Part of the reason the organizations gained a foothold was because campuses were getting much larger. There were so few students that there wasn’t a need to belong to a smaller, more exclusive group.
Popular culture - books, TV, movies, etc. - exalted Greek life as a pillar of college culture but the influence of the groups waned in the 1960s when campus became more diverse and students became more politically active. (Not to say that Greeks were not politically active.) But then fraternities and sororities targeted towards new populations (Latino/a, Muslims, LGBT, “plus size” women, and Asians, to name a few) started to emerge.
I would still say that a sizable number of the students who are active campus leaders - your student body president types, big man/woman on campus types - are Greek. But they’re not the majority by any stretch of the imagination. On large campuses Greeks are very prominent on the social scene (they had the resources and spaces to have parties), athletics (a lot of the groups have one or more intramural teams), and philanthropy (organizing clothing drives, building Habitat for Humanity homes, and fundraising).