Quantum entanglement, in a nutshell, means that the properties of one particle can be deduced by examining the properties of a second particle – even if they are separated by a large distance. As the Nobel committee pointed out, an easy way to imagine this was to think about being given one of two balls – one of which is white and the other black. If you receive a white ball, you know the other ball is black.
Importantly, however, the properties of each particle are not fixed until they are examined – in the ball scenario this would mean that both balls are grey until looked at, whereupon one turns white and the other black.
This lies at the heart of the “spookiness” – rather than “action” at a distance, the two particles, or balls, appear to be inherently connected, without the need for any signal to be sent between them.