Pay-per-click advertising is a fairly simple concept. Search engines such as Google let businesses or other ventures purchase listings which will appear alongside normal, non-paid search results when someone enters keywords relating to that business or service. The main thing that differentiates pay per click from normal online advertising is that the advertiser only pays only for every time that someone clicks on the ad.
Meanwhile, the ad spaces are sold in an auction format. Advertisers bid as to how much they want to pay for a click on their ad, and the highest bid gets the highest position in the listings.