Homology: Why Boundary of Boundary = 0 ?

This equation puzzles most people. WHY ?
$latex boxed {{delta}^2 = 0 { ?}}&fg=aa0000&s=3 $

It is analogous to the Vector Algebra:
Let the boundary of {A, B} =
$latex delta (A,B) = overrightarrow{AB }$

$latex overrightarrow{AB } + overrightarrow {BA} =overrightarrow{AB } – overrightarrow {AB} = vec 0 $

Source: http://mathoverflow.net/questions/640/what-is-cohomology-and-how-does-a-beginner-gain-intuition-about-it

Note: Co-homology: (上)同调

Euclid Geometry & Homology:

Isabell Darcy Lecture: cohomology