I wont claim to be an expert, but from what i know of the practice, sites with ads displayed are payed by the number of times the ad is clicked. So, I get 1 cent for every click. As a result, you get a whole host of scams meant to defraud the system, which is generally pretty easy to do, even if it's done by something like "per unique ip address in a 24 hour window" (ie, every day only 1 click per ip address counts towards what you earn). The theory is that you when you click on an ad, its because you're curious about its content, like checking out items mentioned in tv ads when you go to the store. Once you're on the website the ad redirects to, you're likely to explore and see more of the site. That said, the problem is that there are so many sites trying to trick you into clicking on ads that most users consider them to be akin to spam mail, especially pop-up or embeded ads. As a result, even rotating banner ads are ignored by people who might otherwise be interested.
This raises the question: why then do people still pay for ads to be displayed? Well, in many cases its just to raise awareness. For example, during the elections there were Vote Obama and, to a lesser extent, Vote McCain banners everywhere. You'll also see ads for things like upcoming MMOs and movies, along with tv shows, brands, companies, etc. The goal isnt to necessarily to get you to buy General Mills Cereal (as an example), as you might hope with tv ads or promotions in the sunday paper's coupons, but rather to get people thinking about your brand, so that sometime in the future they'll see a choice between General Mills or a generic brand and remember seeing their brand somewhere else, and pick up the advertised product as a result. Basically, when given one or more alternatives, the most heavily advertised is the most heavily examined, and in theory the more familiar you are with something, the more likely you are to pick it out of a list of choices, even if it isnt the cheapest or best option.
As for the "Click ads to earn money" thing, that's just a way to cause click fraud, and mostly likely is a scam itself. Its an easy way to indirectly cause unique ip clicks, and since there isn't a very good system to track who redirected a user to a site, it results in more money for the scammer with less likelyhood of getting caught. When you figure each click is worth a few cents at most, that limits your earnings substantially. Even so, its still a common practice as far as click fraud goes. But its definently legally questionable, and won't earn you much money, if any at all. Although if youre interested, I know a bank in Nigeria who could use your assistance with a small matter....