Paid results are the results that you see at the top of the page that have a green [ad] icon next to it.
Statistically in 2012, only 6% of all search clicks fell on ads (source)
. Since Google makes direct profit from AdWords, today this number has to be higher due to the constant push of AdWords into the masses. This, however, does not change the fact that most people are reluctant to click on sponsored content (AdWords)
Organic search results, on the other hand, are the results that appear below the ads. How does it work? The Search engine pulls relevant web pages that best correspond to the searched keyword. The results rank based on the search engine algorithm that takes hundreds of different metrics into account to evaluate and pull forward the best (in the eyes of the search engine) result to satisfy the search intent.