An egg is the first stage of a dragon's life cycle. Eggs can be stolen from the cave (known as caveborn or CB) or bred. If an egg is bred, it will be either one of the parents' breeds or a hybrid of the two. If you cannot take any eggs at the time, the bred egg will automatically go to the Abandoned Page (AP). Only one egg can be bred at a time; the exception to this is during a holiday season, where Holiday dragons will breed multiclutches or multiple eggs of their breed- however users can still only pick just one of the produced eggs, with the rest being auto-abandoned to the AP.
Several types of eggs cannot be caught or bred. Vampire eggs can only be obtained through their unique Bite Breed Specific Action, Guardian of Nature eggs only through the "Summon BSA" action, and Neglected Dragon eggs can only be obtained through a special creation process.
Eggs caught from the cave cannot be abandoned or Teleported until 5 hours after they are caught. Bred eggs or eggs caught from the AP can be abandoned or Teleported immediately.
You can only have a certain amount of eggs on your scroll at a time, with the limit depending on your trophy badge. The default amount of eggs on your scroll is four. After gaining higher badges, you will unlock more egg slots- up to 7 with a Gold Trophy. When you have claimed all the eggs you can, it is often referred to as being "locked", "egglocked" or "scroll-locked" (though this is often used when the user cannot claim anymore eggs and hatchlings). You will also be unable to claim eggs if you have reached the maximum number of "growing things" (eggs and hatchlings). You can always check your status by clicking on the badge while viewing your dragons.
As an egg 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. The time at which an egg or hatchling will die is called the Time of Death (ToD). Eggs are often used for Neglected experiments, which are the act of attempting to "turn" an egg into a Neglected Dragon. Eggs can also be bitten by Vampire Dragons, incubated by Red Dragons, gender-influenced by Pink Dragons, and abandoned with no chance of failure. 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 and essentially be sent to the Abandoned Page. 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. Eggs are more susceptible to sickness in their first 24 hours of life. It is recommended that eggs, especially important ones, be hidden until they are at least a day old. Bred eggs will also hatch faster if kept on the same scroll as their parent, as said by TJ09:
Bred eggs get a small "boost"--they'll hatch easier if on the same scroll as their parents.
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. Some eggs are given custom cracking sequences, such as those of Paper Dragons, Magma Dragons or Gemshard Dragons.
Leetle Trees are technically listed as eggs, although remain permanently frozen on the user's scroll as they are. There are also several Fake Eggs that have appeared over time through gag events, though neither Leetle Trees nor Fake Eggs will hatch.