God does not play dice with the universe.
Einstein was an atheist so I don't have any incentive to harp on that portion of it. However, the point of the quote is that Einstein didn't believe that the universe contained any real, fundamental randomness. He was convinced that if we looked deep enough and understood enough we would eventually see the patterns underlying seemingly random events and would be able to model, calculate and predict them. He was wrong. Quantum mechanics shows that the universe is in fact random and events at the tiniest scales simply cannot be predicted ahead of time even with perfect information (the possession of which is also impossible). When I was 16 or so I had strong feelings on the issue and believed that Einstein was right. It was surely a laughable bit of hubris that I thought I had anything relevant to contribute to the field but that did not shake my beliefs. I made my decision based on the fact that people have considered things to be random and unknowable throughout human history and consistently, without fail, we have been able to model, compute and predict those things. Until quantum came along, that is, and we found out that there are things that are fundamentally random. For the past couple years I have had an uneasy truce with this fact because although it certainly seemed true I had no real concept of the proof of it. This changed when I read The Matchbox that Ate a Forty-Ton Truck.
This book is a marvellous manual of modern physics written for people with a bit of background but without the desire to go through derivations and calculations. Marcus Chown manages to talk about extremely complex topics using a combination of scientific knowledge and simple analogies that stitches together the knowledge the experts have with ideas lesser mortals can understand to leave the reader with a really respectable idea of how things work. I have read a number of 'physics for the layperson' books, in particular when I was 16 and thought I might have something to say on the topic, and this one is by far the best. The trick is to combine 'common sense' ideas and analogies to give the reader a real idea of what is going on but provide just enough raw scientific knowledge that it becomes clear in the end how inadequately these simple models portray what is really going on.
Now I have a decent intuition about why exactly the periodic table has the patterns it does and what that means for the formation of life. I can comfortably say I am at peace with the idea that the universe is in fact fundamentally random because I understand why we know that is true. I am much more in awe of the accomplishments of physicists who model the progression of the universe from the Big Bang onward after reading the sorts of things we have figured out about it and how those ideas came about. In short I am informed, I was entertained, and I think anyone with a curiosity about how things really work ought to have a read of this book.