There is a one-to-one mapping between general ordered trees and binary trees which Lisp uses to represent general ordered trees as binary trees. Each node N in the ordered tree corresponds to a node N' in the binary tree; the left child of N' is the node corresponding to the first child of N, and the right child of N' is the node corresponding to the N's next sibling --- that is, the next node among N's parent's children.
One way of thinking about this is that each node's children are in a linked list, chained together with their right fields, and the node only has a pointer to the beginning of this list.