It's basically just another pet site, with dragons. Buy them, breed them, train them, battle them, put apparel/skins/accents on them, give them familiars, etc. You join an elemental flight when you first start and these flights duke it out in a competition called Dominance every week.
Most people just go for pretty dragons with cool colors, but doing things like making character/fandragons is also popular.
Then there's the usual buying and selling of items and posting on forums that's standard on basically every site.
It works fantastically on my phone (the Coliseum works better on my phone than on my laptop), there isn't an actual mobile version.