Magic? Rocket Science? Constantly Changing Algorithms? None of these.
Google has the same conundrum that you and I have. If a hundred people are selling the same product or service, who is the best to buy from?
The one with the highest, earned credibility is. Like everyday life, the business with the right mix of knowledge (demonstrated through content), presentation (achieved with tailored user experience and delivery), and reputation (mentions from other business websites) wins the right to be on top of Google searches.
The difference between SEO and PPC is the same as owning vs renting a property, respectively.
Renting, i.e. PPC will solve the challenge of bringing traffic, but as the time passes, the rent will keep increasing, as the number of people wanting the same lucrative space increases. Buying, i.e. SEO makes that place on Google search truly yours.
Now imagine what owning that property in the right area, i.e. ranking for the right keywords, does for your branding and image.