There is so much that goes into answering this question. I'll keep it short for the sake of time.
When a website draws allot of traffic and becomes popular without spending any money in advertising is called Organic. To achieve organic traffic has to do with Marketing (non-paid) and SEO.
When we start a project with our clients that are seeking organic results we always start with improving their marketing efforts. Posting on social media profiles, being active members of forums, and groups. We push our marketing content on every platform that we believe will yield the desired results.
With SEO, its not just about content, sure that is a huge factor, but so is the design the website in question, what code is it written in. Are we using the best keywords, are we using the H meta tags correctly, does every image named to represent our targeted keywords? The next step would be to build a link campaign, find other websites that are equal or greater page rank that will exchange links with you.
I hope this helps.