Well, not quite. Anyway, as far as I know, Einstein was using God and Nature interchangeably. Apparently he was religious in his own way: "I believe in Spinoza's God, Who reveals Himself in the lawful harmony of the world, not in a God Who concerns Himself with the fate and the doings of mankind." (from Wikipedia). So what he probably meant is that not only we, lowly and limited humans don't know an outcome a of a quantum mechanical experiment in advance (e.g. which hole will an electron go through in a 2-slit interference experiment), but the nature itself doesn't. Later this was experimentally proven, google/wiki "Bell's inequality". Moreover, the quantum mechanics tells us that, unless we don't bother actually observing said electron, it goes through both slits an once.
There is something very mysterious about it, and there were no end to attempts to construct a "deterministic" version of quantum mechanics (google Bohm), but none succeeded.
To a "layperson" this may be an indication of the limits of human knowledge, the manifestation of the divine. To most physicists it means that we have still a lot to discover, hopefully ensuring gainful employment for decades to come :).
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