Eggs found in the wild are being transported to Berk and kept until needed for hatching.
The Hatchery is specifically designed to provide the warmth needed to hatch a healthy Baby Dragon.

In order to use it, you must reach player level 3.

You can hatch more than one Dragon at a time by using the plus symbol under the egg. The hatched Dragon will go directly into your Roster and Book of Dragons.

Upgrade the Hatchery to be able to hatch Dragons of different colors and rarities.