Basically it's a HUGE waste of time. You try to get rare eggs and group up w/ a bunch of people who do the same thing, and then click each others eggs a bunch so they'll hatch (actually just so the Dragon people can get a TON of ad money), then click each others hatchlings til they grow up, and then you have an ugly pixel picture of a dragon, which you can trade and breed w/ other people's ugly pixel pictures. The more of them you collect, the bigger your E-peen. That's your reward for all that wasted time and ad revenue you've given them.
Sounds like a raw deal? It is. It's supremely stupid.