The different kinds of eggs are:
Egg of Velociraptor-(Smart Carnivore), Tamable
Egg of Brachiosaurus-(Herbivore), Tamable
Egg of Dilophosaur-(Carnivore), Untamable
Egg of Stegosaurus-(Herbivore),bleeballee
Egg of T-Rex-(Carnivore),spawn
Egg of Nautilus-(Aquatic), Untamable
Egg of Plesiosaur-(Aquatic), Tamable
Egg of Triceratops- (Herbivore), Tamable
Egg of Pterosaur- (Flying), Tamable
Each egg needs to be in a certain habitat or biome to hatch. If they are in the wrong habitat they do not hatch and they die. Some eggs needs to be in the desert, some in grassland and some in water.
For your Dinosaur to be tamed, you need to be six or less blocks away from it when it hatches.This is a Brachiosaurus egg. This particular egg needs to be outside in order to hatch. If you place it underground, in water or in a winter biome it will not hatch. You can see the Type of Egg, Status and Hatching Process when you right click on it with a Dinopedia.