What is vertex weighting ?
To say that a vertex is "weighted" with respect to a Bone means that the vertex will move as the Bone is rotated in order to stay aligned with it. At 100 percent weighting, the vertex follows the Bone rigidly. At 50 percent weighting, the vertex moves only half as much as the Bone does.
http://webreference.com/3d/lesson98/
...Which means that when two bones meet there is bunch of vertices in that area that should belong to both bones and move so too. Otherwise you get nasty looking shears in the joints because neighbour vertices can belong only one bone (like in the Blitz3D now). Weighting lets each vertex move more freely, ie "stretch".