In Space, no one can hear you scream
The first step in a Xenomorph's life cycle, is the Ovomorph. Typically laid by the Queen, the Ovomorph is often kept near the Queen in a hive, and laid in the hundreds and eventually thousands. Generally leathery and brown in appearance, the top of the egg splits into four "Petals" that fold out once a sufficient host is near.
Unlike most eggs, the Xenomorph's ovomorph is actually a living organism. While dormant and unmoving, the eggs have a complex system and coexistance with the facehugger inside. The facehugger inside actually is technically dead while inside the egg. When the egg eventually senses a host, it uses enzymes to liquify and activate the acid that acts as the Facehuggers blood, effectively giving it life. Until then, it can hold a dormant facehugger for thousands of years.
As stated before, eggs are living and sense when a host comes close and is available. It is thought that its skin acts like a snakes tongue, effectively 'tasting' when a host draws near. It will then have its petal like flaps open up, as it quickly activates the facehugger surprising the unfortunate soul who got too curious.
Same ol' same ol
Just like every other member of the Xenomorph life span, the eggs also have acid blood as a defense against damage. Also, the eggs seem to have a separate hive mind, and communicate with each other to ensure a host. It is known that there can be specific "Praetorian Eggs" that hold a Praetorian/Queen facehugger and embryos. Should there be no queen present, the Praetorian Egg will be prioritized in order to ensure the future of the species.
As with most thing H.R. Giger put out, the egg had a vaginal opening. Originally the four flaps were two, and intentionally looked like a vagina. This had to be changed to better suit the catholic countries this movie would air in, and Giger changed it to four flaps to "Resemble the cross those catholics are so in love with"
As you can probably tell, I'll be going through the life stages of the Xenomorph in honor of that AMAZING trailer for Alien Covenant,