I think I can see what you're asking about.
The power you get from the wind is the power that you can "catch" in the blades. If the blades are longer, then there is more swept area that is catching power from the wind. Since you get 4x the area for 2x the blade diameter, that's probably what you've heard about.
Once you dive into the details, you'll find out that all the pieces have to be matched up to each other for the whole system to work. If the blades are a certain size, then they will collect a certain amount of power. The electrical generator must be able to take full advantage of that, otherwise the blades rip it apart. If you go too far the other way, such as put tiny blades on a whopping generator, then nothing happens at all, they can't get it to turn over.
Then there is the tower, which must be strong enough for the size of windmill mounted on it, yet not so large that it's too heavy or expensive. The rest of the electrical system is yet another project in and of itself, and requires some labour to maintain.
You know how all those flower-power people say you have to be in "balance"? Well so do the engineers...
Welcome to the site, and enjoy your reading. Please ask questions any time you have trouble finding answers, and especially if you get confused about something. It's bound to happen.