It is portrayed with a possibly damaged wing and horn because in one of the legends you learn in the game is that Kyurem crashed on Earth in some sort of ice comet; this possibly means that Kyurem broke part of its wing and horn when it made impact. Its wings are wrapped around its arms and appear to be made of an ice-like substance. However, an NPC in Pokémon Black 2 and White 2 stated that this legend may be not quite true, and Kyurem is actually the corpse of the original dragon Zekrom and Reshiram split from; which can be stated in the pokédex entries: This legendary ice Pokémon waits for a hero to fill in the missing parts of its body with truth or ideals, which shows that Kyurem wishes to reunite with Zekrom and Reshiram. It has two fins by its neck with a small yellow streak down its head. Ice covers its face completely except for its eyes, which are yellow. Additionally, Kyurem has two other forms in which can be fused with either Zekrom or Reshiram. It can change form by using the DNA Splicers (Drayden's family treasure) to turn Reshiram or Zekrom back into the Light Stone or Dark Stone and then merging with it. The process can also be reversed. In Black and White Versions 2, when under the control of Ghetsis, it appears to turn into some sort of awakened form where it's wings are revealed to be node-like appendages that absorb energy, as well as fiery tendrils of energy which it uses to trap Zekrom/Reshiram, then absorb them.
The people of Lacunosa Town tell the story that long ago, Kyurem would take people from the village and eat them by cooling the night's air. It is possible though that this is just a legend and thus is not true.
Kyurem, along with Reshiram and Zekrom, is part of the Tao Trio. Kyurem embodies vitalism and/or wuji.
When encountered in the wild after navigating through the Giant Chasm, Kyurem is at Level 75. This is the third highest level of Pokémon encountered in the wild after Lv. 80 Arceus and Lv. 100 Magikarp.
In Lacunosa Town, people said long ago Kyurem came out at night and took people and Pokémon away to eat them. It is also said that the villagers built large walls to keep Kyurem out, but that wouldn't make sense since it could fly.
Kyurem is the fifth Dragon-type Pokémon to not be weak against Ice-type moves, the first being Kingdra, the second being Dialga, the third being Palkia, and the fourth being Reshiram. All of these Pokemon, except Kingdra, are legendary Pokemon.
Kyurem has the third highest stat total of all Generation V Pokémon, 660 being surpassed only by Reshiram and Zekrom who have equal totals of 680. However, when in either Black or White form, it's stat total jumps to 700, being the second highest stat total of all Pokemon, second only to Arceus.
When caught, Kyurem holds the Comet Shard, an item also found within its lair, the Giant Chasm. It sells for a whopping 60,000 if sold to the ore collector in Icirrus City.
Reshiram, Zekrom and Kyurem share a remixed version of one battle theme. Reshiram's has a fire effect and Zekrom's has an electricity effect, but Kyurem's has a bass playing in the background instead.
No other Pokémon has the same type combination as Kyurem.
Kyurem's species may be the Boundary Pokémon because it may keep Reshiram and Zekrom from fighting each other, acting as the "peacemaker".
In Pokémon Black and White Versions 2, Kyurem changes its form with the use of the DNA Splicers. If you have Zekrom in your party, you can fuse it with Kyurem using this item and it will change to Black Kyurem. If you have Reshiram, it will turn into White Kyurem. Zekrom/Reshiram will disappear from your party, but the process can be reverted at any time using the DNA Splicers.
Its the only Pokemon so far that can fuse and change form at the same time.