Metroid Eggs were described in detail in the Metroid: Other M art gallery.
According to the Metroid instruction manual, the Galactic Federation research team that first charted SR388 discovered the first Metroids in a state of suspended animation. Although they were contained in what was said to be a "capsule", it is possible this was in fact an egg.
Metroid Eggs superficially appear similar to Xenomorph eggs from the Alien series, although they crack open rather than peel outward like a flower.
Using Secret Worlds, Samus can come upon the egg from behind. It is programmed to hatch when Samus is several pixels away, meaning it can hatch from either side.