These different coloured dinosaurs in mario games called yoshis are a big help in certain levels. They can defend you by eating enemies like goombas,octoombas and koopas.
Yoshi eggs  are white with spots of the colour of the yoshi inside. In some games like super Mario flash 2 yoshi eggs are in mystery boxes and they hatch into yoshis automatically after you jump under the mystery box but in some games with only one yoshi called Yoshi like super Mario galaxy 2 you need to jump on the egg to hatch Yoshi.

As mentioned in the first paragraph,yoshis are different colours.Yoshi is a green yoshi and Mario's helper,some of the other yoshi colours are blue,pink,yellow and red.