"And it says that if it comes about that the child is tempted, as Eve was, then she is likely to fall."

Michaelangelo Fall of Man
Public DomainMichaelangelo Fall of Man

This relates to the idea of original sin and the fall of man. In these set of events Eve is represented by Lyra, Adam by Will and Mary Mallone takes the role of the Tempter. While religious teaching regards the fall of man and embrace of knowledge as intrinsically bad, Pullman appears to be taking a far more humanist view in embracing all life has to offer while on the planet.

The story of the fall is the focus of one of Pullman's main inspirations, Milton's Paradise Lost, and explores in depth Eve's fall.

For more information, there is, as always, a very helpful Wikipedia post to start you off.