Pokemon Eggs can be found at Pokestops, and you get to keep the Pokemon found inside once you have placed it into an Egg Incubator and walked the required distance.
Eggs will require you to walk 2KM, 5KM, or 10KM. Once you have walked this distance the egg will hatch and the Pokemon inside is yours!
What will hatch from my egg?
The distance you have to walk for each egg decides which Pokemon you have a chance of hatching from a set loot pool. Use this infographic to decide which Pokemon Egg to incubate next to increase your chances of getting the one your after!