An Egg is the first stage of the Xenomorph's life cycle produced by the Queen through the use of her eggsack, it serves as an organic capsule for the facehugger.
When a host approaches, four "petals" at the top of the egg open up, and a facehugger launches out. The Space Jockeys used an anesthetic mist to put them in suspended animation for safe handling.
When no host approaches, the egg develops several tendril like roots, probably for nutrient absorption similar to plant organisms, to help it sustain itself until a potential host appears. ~ Alien Wiki