The normal, modern-day world where you and I live. The dragons call it "Mundania", or the "Mundane Land". As far as they are concerned, a realm without magic is of no use to them, and therefore not worth their attention. There's nothing strange or unusual about that - right?
The planet Earth is a particularly unique realm in that its mana field has shriveled up, and therefore cannot sustain magic. What little magic there is, has been brought over by immigrants from other, more magical realms. Without a persistent magical field, this imported magic eventually decays, leaving the children and grandchildren of magical denizens with nothing but stories and the faintest whiff of their ancestral blood.
Only non-magical creatures can thrive on the current planet Earth, although there exist possible archeological evidence a past mana field mature enough for proper magic. Non-human races will find it difficult to keep marrying within their bloodline, and even that can only stave off magical entropy for so long without fresh blood from the motherland. Nonetheless, life finds a way.
Yes, the land ruled by dragons is called Dragonia. Yes, they pulled an Alexander and named their homeland after themselves. It was intentional, and the egomania has not escaped the notice of others.
Unlike Earth, Dragonia has a bountiful mana field, and is the origin for many fairytales that Earth-bound humans are familiar with. Magical energy, or mana, can be channeled through many different methods. Some creatures actively manipulate this energy to cast spells and set wards. Others passively channel it through their bodies, resulting in greater-than-average sensitivity to these energies.
There are many magical creatures that dragons permit to live on their land, so long as they agree to serve the dragons and maintain the hierarchy of power. There are dragons, of course - many kinds, many cousins, many clans, many feuds - as well as humans, elves, dwarves, orcs, fairies, mermaids, centaurs, and giant snails.
Not-Dragonia, aka, the Barbarians, aka, Unclaimed Territory
The entire realm is not ruled by dragons. In fact, a reasonably objective person might even point out that Dragonia's sphere of influence has been shrinking for some time now. The further you get from the capital city of the dragons, the more likely you are to find independent cities and towns - maybe even an occasional dragon that doesn't care for the Red Queen's politics.
Though the dragons call any area not under their power unclaimed territory, and those people barbarians (at least, that's how those particular growls would be translated to us puny humans), there's obviously many areas in the world, each with their own name and culture.
For example, there's the Glassy Hills - lovely little farming province back in the day, until there was a revolt over how many sheep to sacrifice to the dragons, and how many to keep for food for the peasants. Now there are no more peasants, no more sheep, and no more crops. The hills have been glassed over by dragonfire, and as far as the ruling class is concerned, the problem has been solved.