You can quite often find Eggs in the wild, by interacting with the PokeStops, which also give you free items.
There are different kinds of these eggs, and they can hatch into a number of Pokemon. If you want to hatch them you will need to work for it. The hatching process can start with putting the egg into an Egg Incubator. This item allows you to hatch an egg after a certain number of steps or kilometers. This is all tracked through your phone’s GPS and Pedometer.
As of this moment, there are four types of eggs: 2km, 5km, 7km and 10km.
To see your eggs, go to your Pokemon list and click on the tab that reads “Eggs”. Click on whichever Egg you want to hatch and a window will appear with all the Incubators you own. Click on the Incubator you want and the process of hatching will begin. The fresh starters have only one Egg Incubator in their inventory, but you can buy more from the Shop, or get rewarded for reaching a new level. Your starting Incubator has unlimited uses, while the ones you buy, break after 3 uses.
When the Egg is placed in the Incubator, it will give you an information on how many more km you must walk if you want to hatch the egg. The GPS is synced with the pedometer your phone has, so it is impossible to trick it by going into your car and driving a few kilometers. If you want the game to count the steps, it must be open and you must walk. Faster moving will not be counted.
It is helpful to think of the eggs as “hidden Pokemon.” The game has already determined which Pokemon the Egg will be, so it only reveals what the Egg has since the beginning. This means that all of us have 9 hidden Pokemon in the inventory. Everything has already been determined, their IVs, movesets, types and etc.
Eggs count toward your Pokemon collection and you can prevent collecting more Eggs by having a full collection. Meaning that if you want to clear out your eggs then you can walk your current ones to hatch them but block getting more when spinning pokestops / gyms or when getting gifts by keeping your pokemon storage full.