According to Wikipedia, Google AdSense is an ad serving program run by Google. Website owners can enroll in this program to enable text, image and, more recently, video advertisements on their sites. These ads are administered by Google and generate revenue on either a per-click or per-thousand-impressions basis.
Google’s Adsense allows for the advertising of other websites that has the same niche as your site. As more people click on the advertisements on your site and they go to the site of the advertiser, you earn some money. Advertisers will pay for traffic that came through your site.
Google is a name that many web users know by heart. Its years of service have built it a reputation that is one of the most reliable in the internet world. That is why you can be sure that having and using Google Adsense can make you earn extra money.
Why should you sign up for Adsense?
First, because AdSense is a very simple and proven solution that already pays for hundreds of thousands of blogs/websites accross the world!
Also, AdSense is provided to you by Google which not only makes it reliable but also trustworthy. Once you have earned money from Google, you can actually trust them to pay it to you!
Finally, because the ads will be contexual, i-e they will be relevant to the content of your blog/site. This way, your visitors will not be offended for seeing the ads on your site.