In the simplest possible sense, if you're frequently visiting sites about cars, you might see more car ads while you browse the web. It's done through a cookie which stores information on which sites carrying AdSense ads you've visited. Google calls it interest-based advertising; it will be rolled out gradually, starting with a small subset of users, and expanded later.
While this is not anything new in the world of online advertising, all eyes are set on Google due to privacy concerns. Users may ask themselves: What information is stored about me when I browse the web? Can i change it? Can I choose not to be a part of this?
Fortunately, the answer to all of these questions is yes. Google will let users see and even edit what information it has gathered on them; it will also let anyone opt-out of interest based advertising altogether. Furthermore, you will not see ads based on your race, religion, sexual orientation or, to a certain extent, financial or health problems.
Of course, most users won't bother to opt out, and they simply won't care about what info Google is storing on them. Warning signs on cigarette packs don't stop most people from smoking, which is proof enough that warnings often aren't enough to change people's habits. Privacy advocates will probably point out that instead of opt-out, Google could have made the program opt-in, by asking users whether they want to join the program or not.
On the publisher end of the deal, they can also choose not to be a part of the program. Some might not want to give information to Google that can potentially help their competitors reach the users. It will, however, probably all boil down to profits: if the new system works better than the old one, no one will complain.