Here's an example. Imagine you have two cards, an ace and a king. You shuffle them, and without looking, you deal one card to yourself and one card to me. Then, you hop aboard a spaceship and fly many lightyears away, leaving me behind on Earth. You wonder to yourself which card was left behind on Earth. Even though we're lightyears apart, there is a way to measure my card instantly: you can simply look at your card and infer that I have the other. Upon seeing that it is a king, you can instantly conclude that my card is an ace. That 'conclusion' was able to travel faster than the speed of the light because it was based on correlation, but not causation. Your card was correlated with mine (knowledge of yours gave you knowledge about mine) but your card did not affect mine (e.g., erasing it and drawing an A on the corners would not turn mine into a king).
(This example, I hope, illustrates the difference between spooky correlation and causation. However, it is misleading about what really goes on in quantum mechanics. In quantum mechanics, the identity of our cards is not fixed after the deal, but remains in limbo until it is actually measured. And this limbo-like superposition state can be measured in different non-independent ways and these probabilities interact with each other and other probabilities. Nonetheless, even with all that added machinery, the general principle of correlation vs causation is the same as the two card example.)