In terms of Heisenberg's uncertainty principle, Einstein was saying that if one were to use a precise measurement of one particle's momentum to determine the precise momentum of the other, then this must increase the uncertainty in the position of the second particle. If, conversely, one were to determine the first particle's position precisely, this must increase the uncertainty in the momentum of the second particle. And these changes must take place instantaneously, through some kind of faster-than-light signalling.
Which is exactly what Bohr argued to be true. Bohr believed in non-local reality: the two particles really do 'co-operate' in a sort of conspiracy forced on them by the nature of physical reality. Schrödinger promptly dubbed the new notion 'entanglement'.
It was completely unacceptable to Einstein. He believed in local reality … . In a private letter to Born he said he simply could not credit the existence of "spooky actions at a distance".