Generating "infinite" randomness from a constant number of sources
This is a great question, Suresh!

Our randomness expansion result does not imply any complexity theoretic result. Here's one way to understand the result: we believe that quantum mechanics governs the world, and under this assumption, there are quantum devices that generate genuine, true, information-theoretic randomness.

However, imagine that you're mistrustful of these boxes that claim to do this wonky quantum stuff and generate randomness (for some, this may not take too much imagining). You don't want to deal with qubits. All you understand are classical bit strings. 

Randomness expansion is a protocol where you, as a classical verifier, can interact with a bunch of black boxes (think of them as non-communicating provers), and after running a protocol with these black boxes, you've certified that their outputs contain very high entropy -- if the provers pass. Furthermore, the amount of randomness you started with is much less than the output entropy you certified. 

In other words, it's an interactive proof for randomness generation. 

So, the only "derandomization" aspect of it is to argue that the protocol itself requires small startup randomness. But the outcome is very un-derandomized: the output produced by the boxes is true randomness, not pseudorandomness (i.e. no computational assumptions).