Not really a god, but more like a figure in the Indian religion/Buddhism.
Acrodding to the religions, there are 6 worlds in this world. The world of human, the world of gods, the world of the dead, the world of hunger, the world of the fallen, and the world of the kill. Ashura is the representative race (?) of the last world mentioned. Ashura is a demon in the Indian religion. However, in the buddhist, it's actually a god.
That's all I know. I'll now proceed to translate what I get from a buddhist book I'm have on my lap:
Spoiler for long long paragraph:
Ashura, a divine race the fights against the gods. This race is a special one--where the males are very ugly, the girls are very pretty. They have extremely good luck, though very aggressive. A race that gathers the best and worst personality together. The buddhist calls the Ashuras 'unholy' or 'fallen gods'.
However, Ashura is different from ghosts and demons, although sharing many similarities(in the negativity way). They have emotions like humans, though they are not human. A race that is not holy, not demonic, nor human. A extremely ugly monster.
According to the legends, Ashura is the demon at the highest level which opposes the gods, and were thus banished from the heavens.
The king of Ashura often leads their race to fight with the king of the gods, because the race of Ashura has lots of beauties, but lacking in good food; while the gods have lots of good food, but lacking in beauties. These two race envy each other and often try to rob each other. Everytime these two races fight, they tend to mess up the earth and the skies(a.k.a. human world). And thus people call a battlefield with lots of dead bodies the 'Shura Area'. In the end, the Ahuras lost, and went into hiding into a lotus seed.
The king of the Ashura is very influential, and very powerful. Always saying 'The more chaos, the better'. He is, also, very malicious. Never trusting anyone, even the buddha himself.
Funny enough, the world of Ashura, along with the world of human and the world of gods, are the three 'good world' in the Buddha religion.
The reason Ashura is used in the sub-title is because of the destiny of the HiMEs, where they have to kill other HiME's beloved (Sakiya REALLY did kill everyone)
Oh, and Unmei no Keitojou is probably the sub-sub-title? We often ignore the word Ashura, since it sounds so horrible and scary.