I'll try to explain with twodimensional example over points. ASCIIart:


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 3rd (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 1st quad of parent node. So, each node (except root) will have a limitation in its quadrant. To transfer that limitation the traversalValue is used.