Why did Obama pick Hillary Clinton?

This is exactly the kind of detailed political question I don’t follow so let’s try some crude, fact-poor economism.  Hillary Clinton commands the loyalties of significant segments of the Democratic Party.  The implication is that Obama will need these segments for what he is trying to do.  Since Obama already has 58 (?) Democratic Senators on his side, we should conclude that Obama will try to do lots in the first few months of his term; this is the "throw long and deep" scenario.

He can always encourage her to leave later, if the relationship does not work out.  Latinos, on the other hand, are stronger as voters than as a lobby or as an organized segment of the Democratic Party.  The implication is that they will get relatively little at the beginning of Obama’s term — when lobbies are needed — but successively more as the next election approaches.

Addendum: Andrew Sullivan considers other hypotheses.