Most website operators will want to benefit from visitor traffic that originates from search engines. Getting that traffic means getting the website to appear in search results. There are two ways to achieve this:
Search results that come from a good search engine ranking are known as organic search results. Search results that come from paid adverts are known as Pay Per Click (PPC) search results.
Suppose I search for restaurants in Windsor on Google. The first page of results looks like this:

There are two kinds of search result here: organic and Pay Per Click (PPC):

Pay Per Click works like this:
Suppose I were a restaurant owner in Windsor. I've would love people to be able to find my website by searching for restaurants in Windsor. Let's look at the organic results for this search term more closely:

The news is not good: all of these results - and those of the send page of results - are from "directory" websites. Directory websites tend to have a lot of information, and also tend to attract a reasonable number of links from other websites. These factors help them to rank well on search engines.
Although it is possible to compete with these directory websites in organic search results, it takes time and effort: all of the activities that fall under the umbrella of "search engine optimisation."
Looking at the again at the PPC results:

This is more encouraging:
Organic and PPC have the same starting point: the selection of keywords (the words and phrases that people search for) that we can successfully compete for.
So far, we're talked about getting onto the search results page. The next task is to get people to click though to your website.
Ah... if only it were that easy! Which is better will depend on each situation; many websites use a combination of both to great effect.
Most websites will benefit from developing strong organic results over a period of time. For websites in the early stages of development (i.e., yet to be ranked by the search engines), PPC can be good for immediate results. PPC can also be great for very targeted (or short-term) campaigns.