A red egg is used in Barbarian Assault to hurt penance monsters. If loaded into the egg launcher and shot at penance creatures, it will explode and deal 3 damage to the primary target, and 1 damage to any penance monster within 3 squares of the primary target. A maximum of five eggs may be loaded into the egg launcher at any given time. Both egg launchers share the same reserve of eggs.
Red eggs are most commonly used against stray Penance Runners. They are also very effective against clumps of Penance Healers.
For an exhaustive list of all known sources for this item, see here