Google AdSense is an ad network that allows you to place ads on your website, and profit when people click on the ads. The program can use keywords and other data to place ads relevant to the website content. The ads themselves are sourced from the advertisers using Google AdWords and their Display Network.
When you search for something on Google, there are usually two, maybe four paid ads in the search at the top and at the bottom. These ads are known as AdWords.
AdSense is the same thing, only instead of the ads appearing on the search engine page, they appear on an actual website. Usually they will be in blocks of text, but they can sometimes appear as pictures.