So why should bees, or architects, use hexagons? For bees, making the wax for the walls of the honeycomb is a very expensive business. (A single bee produces just 1/12th of a teaspoon of honey in their entire lifetime. Bees in a hive need to consume 6-8 pounds of honey to produce 1 pound of wax, which means they collectively need to fly more than 6 times around the world to produce that amount of wax!) So understandably they would want to use this expensive resource most efficiently, building the largest cells possible for a given amount of wax.
If you know how much wall you have to use, say a fixed number of bricks or a fixed amount of honey, how should you build your room so that it encloses the largest space possible?