Focus
From Organic Design wiki
The value of a node is obtained by using 0 as the binary traversal key (i.e association which actually means not to traverse anywhere at all). A node's focus is the item in its loop which will receive the next quantum of execution from nodal reduction.
Parent
The node from which a quantum arrives is a node's parent and is accessed via the nodePARENT association. The value of nodePARENT is maintained by nodal reduction rather than by the loop insert/remove functions so that moving a node from one node's focus to another's is an O1. At runtime, the parent of the currently executing this node is also available as a global variable.