In DragonVale for the iPhone and iPad, upgrading the nursery will increase the amount of hatching beds you have to incubate your eggs. The more hatching beds you have, the more eggs you can raise at once.
The only way to upgrade your nursery however is by using gems.
2 Hatching Beds – 10 Gems
3 Hatching Beds – 25 Gems
4 Hatching Beds – 50 Gems
If you’re having a hard time getting gems, check out my other guide for how to get free gems in DragonVale.