I'll try to explain with two-dimensional example over points. ASCII-art:
           |
           |
      1    |    2
           |
-----------+-------------
           |P
      3    |    4
           |
           |

'+' with 'A' represents a centroid or, other words, point which splits plane for 4 quadrants and it strorend in parent node. 1,2,3,4 are labels of quadrants, each labeling will be the same for all pictures and all centriods, and i will not show them in pictures later to prevent too complicated images. Let we add C - child node (and again, it will split plane for 4 quads):
           |         |
       ----+---------+---
   X       |B        |C
           |         |
-----------+---------+---
           |P        |A
           |         |
           |
           |

A and B are points of intersection of lines. So, box PBCAis a bounding box for points contained in 3-rd (see labeling above). For example X labeled point is not a descendace of child node with centroid C because it must be in branch of 1-st quad of parent node. So, each node (except root) will have a limitation in its quadrant. To transfer that limitation the traversalValue is used.