This is one of those stories that shouldn't be a surprise in any way, but certainly has some interesting potential if it comes to pass. Google's ex-CEO Eric Schmidt has admitted to a fact that is in no way a secret: Google would like to take over as Yahoo's search provider. Yahoo has been powered by Bing since the talks with Google failed back in 2010. "Wait a minute!" you may say. "Does that mean that Google wants a bigger search market share?" Well, yeah. Obviously.
Of course, Eric Schmidt saying Google wants to do it doesn't really have any bearing on what will actually happen. The story is getting a bit of extra attention because ex-Googler Marissa Mayer
is now the CEO at Yahoo, but that may not really mean anything. Remember, Mayer left Google. It seemed pretty clear that even though Mayer was Google employee #20, she hit a ceiling at Google, and it is perfectly reasonable to think that there is a chance Mayer would be upset about that. If that's true, it seems unlikely that she would want to jump to make a deal with Google.
The other part of the story that no one seems to be talking about is Google's ongoing trouble with anti-trust claims. Google has already spent quite a bit of time dealing with government inquiries this year, and a deal with Yahoo would make that even worse. Stats vary, but the general consensus is that Google covers between 68-77% of US web searches, and as high as 86% worldwide. A deal with Yahoo would bump Google 10% in the US, and about 7-10% globally. If Google is already troubled with anti-trust claims, a deal like this won't help anything.