Incubators are needed to hatch a Pokemon egg. There are 2 kinds of incubators in Pokemon Go.
The Infinite Use Incubator
You have an infinite-use incubator when you start the adventure. It can be used to hatch an egg as much as you want.
The Limted Use Incubator
The temporary incubator can be used only 3 times. You can get this type of incubator by level up bonus and paying for it.
What You can Get by Hatching?
You can get the following 3 things by hatching an egg.
Pokemon
Stardust
Candy
1. Pokemon
You do not know what Pokemon you will get from the Pokemon Egg up to finishing hatching. Pokemon from each egg is assigned CP randomly.
2. Stardust and Candy
The amount of Stardust and Candy you can get by hatching Pokemon egg is much larger than that by capturing wild Pokemon. So, incubating and hatching are important for getting those items.
Tips for Hatching Pokemon Egg
Riding a Bicycle
The speed limit for hatching egg is 24km/h to prevent cheating such as driving a car. To earn hatch an egg faster, you need to do walking, running, or riding a bicycle.
Using temporary incubator for 10km eggs
Since you can hatch 3 eggs per limited-use incubator, you should place 10kem eggs in such incubators. That means the limited-use incubator works for 30km.
List of Pokemon from Eggs
There are 3 kinds of eggs: 2km (1.25 miles), 5km (3.1 miles), and 10km (6.3 miles). The longer the distance is, the rarer Pokemon shows up. Here is Pokemon hatching chart.