In spite of the fact that virtually everyone who uses a computer these days has seen it, there are still a lot of folks who don't really understand what search engine advertising (SEA) is. Many more know what it is, conceptually, but don't really understand how it works. I've been a big fan of SEA for well over a decade, and have seen it do some amazing things for profitability. I've also seen it done very poorly, and in those cases, it can result in big waste of money, typically when the advertiser doesn't understand how it works or is impatient with the process.
Search engine advertising is most readily seen as those postage-stamp sized text ads that you see on the side of search engines. You will also see these "sponsored ads" or "sponsored links" on other non-search engine websites. Regardless of what you call the ads, they are presented by search engine technology like Google and Yahoo! and Bing, and the advertiser typically pays by the click.
Unlike most other forms of advertising, the great thing about search engine advertising is that you only pay for it when it "works." With other forms, you pay to run the ad for a period of time regardless of how many prospective customers actually see or respond to the ad. But with search engine advertising, you only pay for the ad when someone not only sees the ad, but actually takes action, e.g. he/she clicks on the ad and goes to your website. The practice is called pay-per-click. As the advertiser, you decide what your budget is (how much you're willing to spend per day) and how much per click you're willing to spend (what is the maximum amount you want to pay for someone to come to your website). As the advertiser, you create the ad text, choose the keywords that best describe your product (or those keywords that searchers are likely to be using when you want your ad to show up), and determine your budget and maximum cost-per-click. With this criteria, search engine technology presents the ads to the searcher who submits a relevant search.
One of the things that makes search engine advertising so effective is that, unlike other forms of traditional advertising, your ad is being presented to someone who is actively LOOKING for what you're selling. So in essence, you're already presenting your ad to a qualified lead.
To sum up... you're presenting your ad to folks who are actively looking for what you sell, and you only pay for it when they bite. How cool is that?