Kouga is the leader of the Wolf Demon Tribe. He is super fast because he has shards of the Sacred Jewel in each of his calves. Kouga has pledged to make Kagome his woman, much to Inu Yasha's continued chagrin.
The Wolf Demon Tribe Kouga lead was killed off by the Birds_Of_Paradise, and now he only has a handful of men and wolves with him. Kouga's boastful attitude gets him in trouble alot, and his carelessness often gets the better of him-especially when Kagome is involved.
Kouga originally had 3 Jewel shards, but one got stolen by Naraku- part of the reason why Kouga seeks revenge against Naraku.
Kouga appears quite frequently throughout episodes, and often helps Inu Yasha and the crew out while going up against Naraku and his minions.