Pureblood
To understand what being a Pure Blood implies, I've reproduced the explanation that is given by Matsuri Hino in VK.A rare being in his own kind. An unique destiny.
The Vampire race or specie has it owns organization and levels; those levels are split in 5 categories ordered by the amount of vampire blood a vampire has in his veins. In some cases a vampire can gain more blood and level-up but in other cases he can only degenerate and finally turn into a blood-thirsty creature out of control.
At the top of the Vampire pyramid stands a tiny group, an elite group, respected worshiped and also feared by they over-helming power. Those are the Pure Bloods.
A selected group, of which Kaname Kuran is part by born right. The mere title, Pure blood or A-Class already told us the fact this kind of vampire have a special blood, they don't have a single drop of human blood, they're also born vampires and can't be changed to anything else.

It is said somewhere in the manga and repeatedly, that Pure Blood are highly protected by the Council not only because of their special blood and large-numerous abilities but also because of an unknown reason (that could be being hunted down, the war and maybe even cursed) Pure Bloods are becoming rare and unique. This is a highly important matter to the whole Vampire race, because Pure Blood are the only ones that can actually convert humans into vampires. Their blood can also stop D-class vampires turning into E-class, and it's mostly think that Nobles or Normal Vampires can gain some extra power too.
It has been told that this last though is considered a taboo in the Vampire world, sucking an A-class blood is absolutely prohibited and could be punished by dead.
With that said, and Kaname being one of those few special class protected vampires, it becomes a bit more understandable why the Council (Old and powerful vampires "ruling" Vampire matters) don't agree on Kaname standing out their hands and "unprotected" at Cross Academy.
His importance is almost unprecedented for them, and they could do anything to have him back and safe.
Safe meaning they would have him locked in some room like Mad Shizuka... And, Kaname wouldn't be able to do or realize any of his still unknowns plans without them aware of such.
Finally, and to put more sugar on Kaname's class. Pure Blood have the following habilities (so far revealed and some theories):
- Convert humans into D-class vampires biting them.
- Stop the E-class degeneration process, by giving his own blood to a D-class vampire (though it must be the same pure blood that once converted said human)
- Abnormal healing speed and regeneration.
- Most likely strength and speed.
- Ability to make lower vampires of any class to obey and serve them.
- Telekinesis or a special mental power (has been seen earlier on some Kaname's entrance and lately when he wasn't at all in control of a new gained power)
- Supposed to have one or various power over elementals but hasn't been confirmed yet.
A-class means, you were born Vampire and you're entire family line is and had always been Vampires. That's why they are so rare and maybe after centuries of war they have become even more...

