The egg is the first state of a dragon's life cycle.
As it gets views, unique views, and clicks, it will eventually hatch and turn into a Hatchling, but this can only happen if its death timer falls to at least 4 days.
You can only have a certain amount eggs on your scroll at one point, depending on your badge. The default amount of eggs on your scroll is four.
Sometimes, if you attempt to kill an egg, it will instantly become a hatchling, however, it may be so scared that it will run away to the AP. This is known as forcing. If this fails the egg dies and the egg sprite is replaced by a half of an egg that has been cracked.
If an egg receives too many views in a short amount of time, it will become sick, and will die if you do nothing about it. This sickness can be cured by hiding the egg for a specific period of time. Usually, 24 hours is recommended, although shorter healing times have been reported. Sickness on an egg is generally referred to as "softshell" due to the description that appears on the egg when it is sick.
When it is close to hatching, the egg will visually display cracks on it. These cracks will gradually become larger, and later turn into a gaping hole when the dragon is almost done hatching. There are 6 stages of an egg hatching, the first (0) stage is the normal egg and the last (5th) stage is when the egg has a gaping hole.Also, quoting TJ09
Bred eggs get a small "boost"--they'll hatch easier if on the same scroll as their parents.