It is a section of pipe insulation.

I special order it online, Lowe's doesn't carry that size. I can look it up if you are interested in knowing. I stuff some paper towel or bubble wrap in the bottom, slide the egg in, and stuff some paper towel or bubble wrap in the top. No other packaging required, and it costs me about $5-6 to pack a dozen eggs. I use the flat rate shipping boxes so the tubes are always the exact same size, a medium box holds 14 tubes (for 12+ orders) and a large box holds 26 if I remember right. I can cut a bunch of tubes in early spring and put them in a big sack next to a stack of flat rate boxes which are free from the post office, add a roll of tape to the pile and I can knock out a bunch of egg orders at once that way. Flat rate shipping labels printed from USPS.com, paid through my paypal account, and then drop them at the counter at the post office. It's the easiest way I've found.
ETA: I always write on the invoice that is set on top of the eggs warning the buyer that the eggs are not taped in and to remove each tube SLOWLY.