Eggs, specifically called Tamagotchi Eggs, are vessels of life in which all the Tamagotchis were born from. Eggs are made after a male and female mate, which holds a growing life waiting to be born in the world of Tamagotchi.
The Tamagotchi egg is a small circular object, larger than a chicken egg, but still small enough to fit in a human hand. It's structure is very smooth and solid. Eggs also come in a variety of patterns and colors.
Inside the egg is a developing Tamagotchi embryo. It settles inside the shell where it stays warm and protected. Once the embryo is fully developed, it hatches into a young baby Tamagotchi. An egg usually hatches within a few days of being laid.
Eggs are very fragile. But it is unknown what happens if the contents gets compromised after the shell shatters.
In the Anime
The Tamagotchi eggs exists in the anime, but are rarely featured. Unlike in the game, Tamagotchi eggs and the baby inside glow brightly while hatching. The shell cracks, and then explodes.