Adwords is Googles version of the pay-per-click advertising model. It allows you to display ads which link directly to your website when searches are done for your chosen keywords or key phrases. These ads are located to the right of the results which Google gives you for a search and they're also displayed on Googles many partner sites which include AOL, Earthlink, HowStuffWorks and blogger. Recently with the launch of Googles Adsense program your ads could also be displayed on websites related to your keywords.
When you create an Adwords ad, you choose keywords for which your ad will appear and specify the maximum amount you're willing to pay for each click. Remember Googles Adwords program uses a PPC model so you only pay when someone actually clicks on your ad and hence visits your website. Adwords enables you to save money as its program Discounter automatically reduces the actual cost per click you pay to the lowest cost needed ($0.01 above competition) to maintain your ads position on the results page.
Google is competing well in this arena, in fact they now dominate the market, pulling more advertisers and revenue than former industry leader Overture.com does. I don't know how long this will last though as Yahoo INC! has just bought Overture. What has Yahoo got up its sleeve?