Octrees are one of many ways to divide the space into smaller volumes structured in a tree. This is useful for culling objects while rendering or for finding collisions between objects. First cover the entire space that is of important into one big cuboid. Then the dividing algorithm for the tree goes as follows:

- First select the maximum number of objects in each cuboid. This determines how deep the tree will go.

- For each cuboid that contains more objects than the maximum allowed, split it into eight (oct = eight) new cuboids with the same volume and dimensions. Repeat this step until all cuboids fulfill the requirement.

The procedure looks like the following:

More information about octrees.
http://www.gamasutra.com/features/19970801/octree.htm

Source of the image:
http://en.wikipedia.org/wiki/Octree

A little description of octrees.
http://www.flipcode.com/archives/Introduction_To_Octrees.shtml