The Information, Larry Page hasn't yet created the Google Y research lab, but has proposed the idea. Google Y would take on projects like creating a more efficient airport, and even building a model city.Page reportedly wants to take on more long-term projects, and with Google 2.0 wants to tackle the biggest challenges facing humanity and how Google can help overcome them. Calico is part of that initiative, since death is probably one of the top "challenges" of being human (if you see death that way). According to
Those seem like pretty large scale ideas, but the plans for Google 2.0 and the Y lab can get very small as well. Page reportedly wants to get location tracking to be precise "down to the inches." The idea appears to be to create something like iBeacon, so you could identify those close by, and get personalized service while shopping. There are also plans for biometric security to replace traditional passwords, but that is something that has been on Page's mind for a while now.
It is incredibly impressive to see Larry Page attempting to honestly change the world, especially since so far he's been able to convince investors to let him work on these projects that don't necessarily have traditional business plans behind them.