Eggs can be found on the PokéStops, GYMs, and on weekly Adventure Sync events. Also a gift your friends send may have one in it. They will hatch after travelling certain distances. The Pokémon hatched from Eggs apparently have higher IV's.
|12 KM Eggs|
|10 KM Eggs|
|10 KM Eggs (Adventure Sync Rewards)|
|7 KM Eggs|
|5 KM Eggs|
|5 KM Eggs (Adventure Sync Rewards)|
|2 KM Eggs|