The Voronoi diagram is a set of points and lines that form essentially (for lack of a better word) a grid. In it, a single point lies within each set of geometry that is created from the lines, never touching the lines. For a much, much, better explanation of it, go here.
This is a flash voronoi diagram that you can play around with. Its very interactive and is a lot of fun making points fly across the screen (which are actually a series of points – not just one) Go here.
From Wiki: It is named after Georgy Voronoi, and is also called a Voronoi tessellation, a Voronoi decomposition, or a Dirichlet tessellation (after Lejeune Dirichlet). Voronoi diagrams can be found in a large number of fields in science and technology, even in art, and they have found numerous practical and theoretical applications.