The photos are of the perennial favourite Egg Toss Game where partners line up across from each other and toss a raw egg back and forth. See the egg in the top centre of this photo:
Tossing the egg comes in many forms, but the key word is 'gently'.
Likewise, there are many ways to catch the egg without it breaking. In the following photo, 2 eggs are in the air... the first is above Nelson's head, the second is on the right side of the photo.