They are laid by tamed or wild Moa mobs, akin to Chickens. Moas are uncommon, so one may have to search a fair bit before they find a Moa. They are also uncommon Dungeon chest loot.
Moa Eggs have to be placed inside an Incubator, using Ambrosium Torches to warm the egg. After a while, the egg will hatch, and a Baby Moa will spawn. Feeding the Baby Moa with Aechor Petals will make it mature into an adult. Four for a Blue Moa, six for White Moa, and eight for a Black Moa.
Moa Egg's data values are:
4546 (dec), 11C2 (hex), 1000111000010 (bin)
Issues relating to Moa Egg are maintained on the bug tracker. Report issues for Moa Egg there.