Honeycombs are mainly used to build Bee Boxes and craft Beeswax, but can also be used in Taffy, Pumpkin Cookie, and Ice Cream recipes as a substitute for Honey or as a neutral filler in any other Crock Pot recipes. However, Honeycomb itself cannot be eaten.
The ideal time to get it from Bee Hives is right before Dusk when most or all bees are outside collecting pollen. The only ones that defend the hive are still inside until the player fights back, and one or two bees can be safely ignored with protective gear. Since Killer Bees don't leave their nest to collect pollen, there is no opportune time to attack a Killer Bee Hive, except for leading other mobs like Deerclops into them, to access its honeycomb.
Another option is luring them away by proceeding to run in large circles to keep them a fair distance. Since they are far slower than the player it becomes an easy task (even more so if there is a Road surrounding the nest). Then run back, destroy the hive and take the prize.
In Don't Starve Together, the Gigantic Beehive has a very small chance to drop a Honeycomb every time the player hammers it. The Bee Queen also drops 1-2 Honeycombs upon death, and her Bee Queen Crown also drops 4 Honeycombs when deconstructed.