The Voronoi pattern is basically regions around points such that all the area in each region is the closest to the point it surrounds. So if you have just two points in space then the pattern is merely a line dividing the region in two midway between them perpendicular to a line joining the two points. As you drop more in then it fractures more into the triangles and polygons.
Natural examples of Voronoi patterns are created with bubbles so that looking down onto a dish of bubbles that are all packed together is a perfect pattern. The bubbles all try to form the least amount of surface tension. Since all the bubbles are made out of the same stuff then they pull on each other until it equalizes to that pattern which is optimal. When one bubble bursts then they all jiggle about and reform the new pattern.
There is an opposite space cutting pattern which is called the Delaunay pattern and it has lines which join up the dots. Actually all the shapes are triangles in this pattern. They use this algorithm to make 3D models from point clouds. You can use it in terrain models by specifying a few height points, stitching it all up with Delaunay and then it has triangles covering the area so it has a complete surface instead of just a few points. I.e. Its really useful !