Pay-Per-Click Advertising (frequently called "PPC") is a form of marketing that involves paying for each visitor to your site. It typically begins at about 10 cents per visitor and goes up from there (often up to several dollars or more).
The adds are minimally shown on the side or across the top of a search engine results page (typically with the words "Sponsored Links") and appear in a light blue or yellow area.
As an advertiser, you bid on a search term. When that term is searched by a potential website visitor, your ad appears. It can appear many times but you only pay when that person clicks on your ad to come to your website.
This gets visitors to a website instantly, not over time as in search engine optimization (SEO). In the long run, when Search Engine Optimization is done properly it is much cheaper and can be more effective, although these two approaches can be used together as part of a larger marketing campaign. The two most popular PPC methods involve placing ads with Google's Adword program and Yahoo's program.