This centaur doctor is basically one of the first NPCs you meet on the site. He explains how the world he lives in works, how breeding takes place, and why you as a pet owner are responsible for the health and well-being of your pets. The egg he's holding is that of a brown centaur, btw.
How eggs work: In this pet-verse, there are only male pets, and as a result no way of breeding. To counter extinction, scientists like Doctor Reed developed a machine that takes the DNA from two parties (a breeding pair) and combines it, gene-splicing it into a new life. The resulting egg will be of either one of the parents, not a combination of the species.
I know how flawed the logic for that is, but this is a concept for a future pet-site, it doesn't have to make sense :B