The modern Easter Egg box was designed in the 1950’s by a couple of Americans who noticed how  light bulbs were packaged.

(Two designers, Bill Horry and John Waddington were inspired by the open cartons used for light bulbs. As they were cheap and easy to make and they provided space and protection for the fragile eggs. Their prototype was developed by Cadbury’s Design Office, and first used for a Roses Easter egg – it’s the origin of all the Easter egg cartons you see in the shops today. I’m afraid these boxes are wasted on me, as I make my own eggs – the only transport problem I have is from the mould to my mouth.)

Source: Cadbury’s