But search ranking is competitive, so naturally, it’s not easy to claim that top spot in organic search. That’s why many marketers and website owners pay to play, and why so many people choose the Pay Per Click (PPC) route. It’s fast. It’s effective. It’s high-visibility for your business. The caveat? You stop paying, and your visibility goes **POOF**.
Clients often ask me the difference and I give them a simple answer that normally puts an end to the conversation and their questions, much like the answer shane thomas gave, but less detailed.  Direct is people putting in your url in the top and organic is people searching for you.  Here is an example: If I want to buy a book i type in amazon.com (direct traffic) but if i forgot where to buy a book online i search for "where to buy a book online" which directs me to amazon.com (organic traffic).  When i explain it like this, a light bulb goes off and they understand.  Hope that helps.
One of the things that can slow-bleed the traffic from your site is the quality (or lack thereof) of the content you publish on your site. Previous Google updates like Panda have already been released specifically to deal with the issue of low-quality content on websites. Long story short: Panda intended to stop sites with bad content from appearing in the search results.

A variety of methods can increase the prominence of a webpage within the search results. Cross linking between pages of the same website to provide more links to important pages may improve its visibility.[47] Writing content that includes frequently searched keyword phrase, so as to be relevant to a wide variety of search queries will tend to increase traffic.[47] Updating content so as to keep search engines crawling back frequently can give additional weight to a site. Adding relevant keywords to a web page's meta data, including the title tag and meta description, will tend to improve the relevancy of a site's search listings, thus increasing traffic. URL normalization of web pages accessible via multiple urls, using the canonical link element[48] or via 301 redirects can help make sure links to different versions of the url all count towards the page's link popularity score.
The term “organic traffic” is used for referring to the visitors that land on your website as a result of unpaid (“organic”) search results. Organic traffic is the opposite of paid traffic, which defines the visits generated by paid ads. Visitors who are considered organic find your website after using a search engine like Google or Bing, so they are not “referred” by any other website.
Remember when you used to rely solely on search engines for traffic? Remember when you worked on SEO and lived and died by your placement in Google? Were you #1? Assured success. Well, okay, maybe not assured. Success only came if the keywords were relevant to your site users, but it was the only real roadmap to generating site traffic and revenue.