Eggs (not Lucky Eggs) are Pokémon that you can acquire from PokéStops. They are not listed with the rest of your items, and instead appear in the second tab of your Pokémon section.
Everyone starts the game with one Egg Incubator ∞, which is colored orange. It may be used to hatch as many eggs as you want. Each incubator can only hold one egg at a time, though, which cannot be unslotted.
You must travel the distance while the game is active or minimized/lock screened when using GO+, or the distance will not count. This is based on GPS-measured distance and not on number of steps like a pedometer.
- Pokémon hatched from eggs appear to have CP based on the trainer level when you first acquired them, so saving them for higher level won't help.
Once the trainer reached level 20, any egg you pick up will always hatch at level 20. This means hatched Pokémon usually have higher CP than most wild Pokémon encounters of the same type
- Pokémon hatched from eggs tend to have much higher IV scores. Individual IVs are well above what is expected of the usual uniform distribution between 0-15 and falling more into the 10-15 range.
The maximum speed that an individual can travel to hatch Pokemon is roughly ~6.5MPH (10.5km/h). Travel faster, such as by car or bike, and Pokemon GO may discard your distance traveled.