Pay per click (PPC) is actually a form of advertising but it accomplishes results similar to search engine optimization. With pay per click programs, you bid on key phrases to determine your ranking. Normally, the more you are willing to spend on a bid, the higher you can rank in the search engines in the PPC listings, which are also sometimes labeled as Sponsored Results.
However, Google Adwords and other search engines also take other factors into consideration such as the quality of your ads and landing pages. Expenses are generated when someone actually clicks on your listing - hence the name "pay per click".
SEO is a more permanent form of optimizing your Web site without paying for your rank position. Both PPC and SEO will allow you to obtain high rankings. It's simply a matter of how you want to go about it.