While it's not a drastic change -- Page was already the CEO of Google once, and has had a leading role since the company's beginning -- it does raise questions of how the company will change under the new CEO.
Formally, Schmidt will focus on external affairs, relationships with businesses and governments as well as customer relations. Page will focus on internal affairs, product development, and technology strategy. But instead of Google functioning as a triumvirate, led by Schmidt, Page and Sergey Brin, Page will now be calling the shots - and taking more responsibility.
It will not be an easy task. The company faces increasing challenges to show it's not monopolizing the search space and that it cares about user privacy. Google needs to convince the world it's a gentle giant: huge but benevolent, successful but not at the expense of its millions of users.
The company has also had a very tense relationship with one of the largest markets in the world, China, resulting in a minute influence even in the space where Google is traditionally the best: search.
Finally, as Facebook grows larger, Google has been unable to prove it can compete in the social space. Google Buzz has been, for the most part, a failure; Orkut hasn't been going anywhere for years; and a rumored Facebook competitor is still just that -- a rumor. Google needs to either succeed at competing with Facebook (through an acquisition or a revolutionary new product) or stop trying, perhaps making strategic partnerships where needed to make sure it keeps a piece of the social pie.