Imagine you want to install ceramics in your house. Suppose that the price is the same, independent on the shape (and the size in terms of area is the same as well) but that the glue is extremely expensive. Then, you want to buy the pack of ceramics that use the least amount of glue to put them together, and that the shape is an admissible shape to cover the floor with no need of cutting them into pieces (like squares, rectangles, triangles… what else?). Pappus of Alexandria, who was born in 350 A.C., suggested around the year 400 that regular hexagons minimize the glue you will need (in terms of perimeter per area, to fill up the plane), but this wasn’t proved until 1999 by Thomas Hales.
What is curious is that bees knew it even before Pappus of Alexandria; they construct their hives using hexagons! (Nature is amazing, isn’t it?)
Recommended video (Talk of Eduardo De Cabezón in TEDx)